1 added
2 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>142 Learners</p>
1
+
<p>152 Learners</p>
2
<p>Last updated on<strong>August 12, 2025</strong></p>
2
<p>Last updated on<strong>August 12, 2025</strong></p>
3
<p>In calculus, differentiation is the process of finding the derivative of a function. It is essential for understanding the behavior of functions and their rates of change. In this topic, we will learn the formulas for differentiation covered in the syllabus.</p>
3
<p>In calculus, differentiation is the process of finding the derivative of a function. It is essential for understanding the behavior of functions and their rates of change. In this topic, we will learn the formulas for differentiation covered in the syllabus.</p>
4
<h2>List of Math Formulas for Differentiation</h2>
4
<h2>List of Math Formulas for Differentiation</h2>
5
<p>Differentiation is a fundamental concept in<a>calculus</a>. Let's learn the<a>formulas</a>to calculate the derivative<a>of</a>various<a>functions</a>.</p>
5
<p>Differentiation is a fundamental concept in<a>calculus</a>. Let's learn the<a>formulas</a>to calculate the derivative<a>of</a>various<a>functions</a>.</p>
6
<h2>Math Formula for Differentiation of Basic Functions</h2>
6
<h2>Math Formula for Differentiation of Basic Functions</h2>
7
<p>The basic differentiation formulas include:</p>
7
<p>The basic differentiation formulas include:</p>
8
<p>1. The derivative of a<a>constant</a>function is zero.</p>
8
<p>1. The derivative of a<a>constant</a>function is zero.</p>
9
<p>2. The derivative of xn is nx(n-1), where n is a<a>real number</a>.</p>
9
<p>2. The derivative of xn is nx(n-1), where n is a<a>real number</a>.</p>
10
<p>3. The derivative of ex is ex.</p>
10
<p>3. The derivative of ex is ex.</p>
11
<p>4. The derivative of ax is ax ln(a), where a is a constant.</p>
11
<p>4. The derivative of ax is ax ln(a), where a is a constant.</p>
12
<h2>Math Formula for Differentiation of Trigonometric Functions</h2>
12
<h2>Math Formula for Differentiation of Trigonometric Functions</h2>
13
<p>The differentiation of trigonometric functions includes:</p>
13
<p>The differentiation of trigonometric functions includes:</p>
14
<p>1. The derivative of sin x is cos x.</p>
14
<p>1. The derivative of sin x is cos x.</p>
15
<p>2. The derivative of cos x is -sin x.</p>
15
<p>2. The derivative of cos x is -sin x.</p>
16
<p>3. The derivative of tan x is sec2 x.</p>
16
<p>3. The derivative of tan x is sec2 x.</p>
17
<p>4. The derivative of cot x is -csc2 x.</p>
17
<p>4. The derivative of cot x is -csc2 x.</p>
18
<p>5. The derivative of sec x is sec x tan x.</p>
18
<p>5. The derivative of sec x is sec x tan x.</p>
19
<p>6. The derivative of csc x is -csc x cot x.</p>
19
<p>6. The derivative of csc x is -csc x cot x.</p>
20
<h3>Explore Our Programs</h3>
20
<h3>Explore Our Programs</h3>
21
-
<p>No Courses Available</p>
22
<h2>Math Formula for Differentiation of Inverse Trigonometric Functions</h2>
21
<h2>Math Formula for Differentiation of Inverse Trigonometric Functions</h2>
23
<p>The differentiation of inverse trigonometric functions includes:</p>
22
<p>The differentiation of inverse trigonometric functions includes:</p>
24
<p>1. The derivative of sin(-1) x is 1/√(1-x2).</p>
23
<p>1. The derivative of sin(-1) x is 1/√(1-x2).</p>
25
<p>2. The derivative of cos(-1) x is -1/√(1-x2).</p>
24
<p>2. The derivative of cos(-1) x is -1/√(1-x2).</p>
26
<p>3. The derivative of tan(-1) x is 1/(1+x2).</p>
25
<p>3. The derivative of tan(-1) x is 1/(1+x2).</p>
27
<p>4. The derivative of cot(-1) x is -1/(1+x2).</p>
26
<p>4. The derivative of cot(-1) x is -1/(1+x2).</p>
28
<p>5. The derivative of sec(-1) x is 1/(|x|√(x2-1)).</p>
27
<p>5. The derivative of sec(-1) x is 1/(|x|√(x2-1)).</p>
29
<p>6. The derivative of csc(-1) x is -1/(|x|√(x2-1)).</p>
28
<p>6. The derivative of csc(-1) x is -1/(|x|√(x2-1)).</p>
30
<h2>Importance of Differentiation Formulas</h2>
29
<h2>Importance of Differentiation Formulas</h2>
31
<p>In mathematics and real life, differentiation formulas are used to analyze and understand the behavior of functions. Here are some important points about differentiation: </p>
30
<p>In mathematics and real life, differentiation formulas are used to analyze and understand the behavior of functions. Here are some important points about differentiation: </p>
32
<p>Differentiation helps in understanding the<a>rate</a>of change of quantities. </p>
31
<p>Differentiation helps in understanding the<a>rate</a>of change of quantities. </p>
33
<p>It is used in various fields like physics, engineering, and economics to solve real-world problems. </p>
32
<p>It is used in various fields like physics, engineering, and economics to solve real-world problems. </p>
34
<p>By learning these formulas, students can easily grasp advanced calculus concepts.</p>
33
<p>By learning these formulas, students can easily grasp advanced calculus concepts.</p>
35
<h2>Tips and Tricks to Memorize Differentiation Formulas</h2>
34
<h2>Tips and Tricks to Memorize Differentiation Formulas</h2>
36
<p>Students often find differentiation formulas challenging. Here are some tips and tricks to master them: </p>
35
<p>Students often find differentiation formulas challenging. Here are some tips and tricks to master them: </p>
37
<p>Use mnemonics to remember the<a>sequence</a>of differentiation formulas. </p>
36
<p>Use mnemonics to remember the<a>sequence</a>of differentiation formulas. </p>
38
<p>Practice derivations regularly to reinforce your understanding. </p>
37
<p>Practice derivations regularly to reinforce your understanding. </p>
39
<p>Create a formula chart for quick reference and use flashcards to memorize them.</p>
38
<p>Create a formula chart for quick reference and use flashcards to memorize them.</p>
40
<h2>Common Mistakes and How to Avoid Them While Using Differentiation Formulas</h2>
39
<h2>Common Mistakes and How to Avoid Them While Using Differentiation Formulas</h2>
41
<p>Students make errors when applying differentiation formulas. Here are some mistakes and ways to avoid them:</p>
40
<p>Students make errors when applying differentiation formulas. Here are some mistakes and ways to avoid them:</p>
42
<h3>Problem 1</h3>
41
<h3>Problem 1</h3>
43
<p>Differentiate f(x) = x^3 + 5x^2 - 4x + 7 with respect to x.</p>
42
<p>Differentiate f(x) = x^3 + 5x^2 - 4x + 7 with respect to x.</p>
44
<p>Okay, lets begin</p>
43
<p>Okay, lets begin</p>
45
<p>The derivative is f'(x) = 3x2 + 10x - 4</p>
44
<p>The derivative is f'(x) = 3x2 + 10x - 4</p>
46
<h3>Explanation</h3>
45
<h3>Explanation</h3>
47
<p>To differentiate, apply the power rule: f'(x) = 3x(3-1) + 5(2)x(2-1) - 4(1)x(1-1) + 0 = 3x2 + 10x - 4</p>
46
<p>To differentiate, apply the power rule: f'(x) = 3x(3-1) + 5(2)x(2-1) - 4(1)x(1-1) + 0 = 3x2 + 10x - 4</p>
48
<p>Well explained 👍</p>
47
<p>Well explained 👍</p>
49
<h3>Problem 2</h3>
48
<h3>Problem 2</h3>
50
<p>Differentiate f(x) = sin x + cos x with respect to x.</p>
49
<p>Differentiate f(x) = sin x + cos x with respect to x.</p>
51
<p>Okay, lets begin</p>
50
<p>Okay, lets begin</p>
52
<p>The derivative is f'(x) = cos x - sin x</p>
51
<p>The derivative is f'(x) = cos x - sin x</p>
53
<h3>Explanation</h3>
52
<h3>Explanation</h3>
54
<p>Apply the trigonometric differentiation rules: The derivative of sin x is cos x, and the derivative of cos x is -sin x. So, f'(x) = cos x - sin x</p>
53
<p>Apply the trigonometric differentiation rules: The derivative of sin x is cos x, and the derivative of cos x is -sin x. So, f'(x) = cos x - sin x</p>
55
<p>Well explained 👍</p>
54
<p>Well explained 👍</p>
56
<h3>Problem 3</h3>
55
<h3>Problem 3</h3>
57
<p>Find the derivative of g(x) = e^x * ln x.</p>
56
<p>Find the derivative of g(x) = e^x * ln x.</p>
58
<p>Okay, lets begin</p>
57
<p>Okay, lets begin</p>
59
<p>The derivative is g'(x) = ex * ln x + ex/x</p>
58
<p>The derivative is g'(x) = ex * ln x + ex/x</p>
60
<h3>Explanation</h3>
59
<h3>Explanation</h3>
61
<p>Using the product rule, where u = ex and v = ln x: g'(x) = u'v + uv' = ex * ln x + ex * (1/x) = ex * ln x + ex/x</p>
60
<p>Using the product rule, where u = ex and v = ln x: g'(x) = u'v + uv' = ex * ln x + ex * (1/x) = ex * ln x + ex/x</p>
62
<p>Well explained 👍</p>
61
<p>Well explained 👍</p>
63
<h3>Problem 4</h3>
62
<h3>Problem 4</h3>
64
<p>Differentiate h(x) = x^2 * e^x with respect to x.</p>
63
<p>Differentiate h(x) = x^2 * e^x with respect to x.</p>
65
<p>Okay, lets begin</p>
64
<p>Okay, lets begin</p>
66
<p>The derivative is h'(x) = 2x * ex + x2 * ex</p>
65
<p>The derivative is h'(x) = 2x * ex + x2 * ex</p>
67
<h3>Explanation</h3>
66
<h3>Explanation</h3>
68
<p>Using the product rule, where u = x2 and v = ex: h'(x) = u'v + uv' = 2x * ex + x2 * ex</p>
67
<p>Using the product rule, where u = x2 and v = ex: h'(x) = u'v + uv' = 2x * ex + x2 * ex</p>
69
<p>Well explained 👍</p>
68
<p>Well explained 👍</p>
70
<h3>Problem 5</h3>
69
<h3>Problem 5</h3>
71
<p>Find the derivative of y = ln(x^2 + 1).</p>
70
<p>Find the derivative of y = ln(x^2 + 1).</p>
72
<p>Okay, lets begin</p>
71
<p>Okay, lets begin</p>
73
<p>The derivative is y' = 2x/(x2 + 1)</p>
72
<p>The derivative is y' = 2x/(x2 + 1)</p>
74
<h3>Explanation</h3>
73
<h3>Explanation</h3>
75
<p>Using the chain rule: y' = d/dx [ln(x2 + 1)] = 1/(x2 + 1) * 2x = 2x/(x2 + 1)</p>
74
<p>Using the chain rule: y' = d/dx [ln(x2 + 1)] = 1/(x2 + 1) * 2x = 2x/(x2 + 1)</p>
76
<p>Well explained 👍</p>
75
<p>Well explained 👍</p>
77
<h2>FAQs on Differentiation Formulas</h2>
76
<h2>FAQs on Differentiation Formulas</h2>
78
<h3>1.What is the power rule for differentiation?</h3>
77
<h3>1.What is the power rule for differentiation?</h3>
79
<p>The power rule states that the derivative of xn is nx(n-1), where n is a real<a>number</a>.</p>
78
<p>The power rule states that the derivative of xn is nx(n-1), where n is a real<a>number</a>.</p>
80
<h3>2.How to differentiate a product of two functions?</h3>
79
<h3>2.How to differentiate a product of two functions?</h3>
81
<p>Use the<a>product</a>rule: if u and v are functions of x, then the derivative of uv is u'v + uv'.</p>
80
<p>Use the<a>product</a>rule: if u and v are functions of x, then the derivative of uv is u'v + uv'.</p>
82
<h3>3.What is the chain rule in differentiation?</h3>
81
<h3>3.What is the chain rule in differentiation?</h3>
83
<p>The chain rule is used to differentiate composite functions. If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).</p>
82
<p>The chain rule is used to differentiate composite functions. If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).</p>
84
<h3>4.How to find the derivative of a trigonometric function?</h3>
83
<h3>4.How to find the derivative of a trigonometric function?</h3>
85
<p>Use the specific differentiation formulas for trigonometric functions, e.g., the derivative of sin x is cos x.</p>
84
<p>Use the specific differentiation formulas for trigonometric functions, e.g., the derivative of sin x is cos x.</p>
86
<h3>5.What is implicit differentiation?</h3>
85
<h3>5.What is implicit differentiation?</h3>
87
<p>Implicit differentiation is used when a function is not explicitly solved for one<a>variable</a>. Differentiate both sides of the equation with respect to x, treating y as an<a>implicit function</a>of x.</p>
86
<p>Implicit differentiation is used when a function is not explicitly solved for one<a>variable</a>. Differentiate both sides of the equation with respect to x, treating y as an<a>implicit function</a>of x.</p>
88
<h2>Glossary for Differentiation Formulas</h2>
87
<h2>Glossary for Differentiation Formulas</h2>
89
<ul><li><strong>Derivative:</strong>The derivative measures how a function changes as its input changes. </li>
88
<ul><li><strong>Derivative:</strong>The derivative measures how a function changes as its input changes. </li>
90
<li><strong>Power Rule:</strong>A basic differentiation rule stating that the derivative of xn is nx(n-1). </li>
89
<li><strong>Power Rule:</strong>A basic differentiation rule stating that the derivative of xn is nx(n-1). </li>
91
<li><strong>Product Rule:</strong>A differentiation rule used for finding the derivative of a product of two functions. </li>
90
<li><strong>Product Rule:</strong>A differentiation rule used for finding the derivative of a product of two functions. </li>
92
<li><strong>Chain Rule:</strong>A method for differentiating composite functions. </li>
91
<li><strong>Chain Rule:</strong>A method for differentiating composite functions. </li>
93
<li><strong>Implicit Differentiation:</strong>A technique for finding the derivative of a function defined implicitly.</li>
92
<li><strong>Implicit Differentiation:</strong>A technique for finding the derivative of a function defined implicitly.</li>
94
</ul><h2>Jaskaran Singh Saluja</h2>
93
</ul><h2>Jaskaran Singh Saluja</h2>
95
<h3>About the Author</h3>
94
<h3>About the Author</h3>
96
<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
95
<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
97
<h3>Fun Fact</h3>
96
<h3>Fun Fact</h3>
98
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
97
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>