Derivative of 10^x
2026-02-28 23:52 Diff
https://brightchamps.com/en-us/math/calculus/derivative-of-10%5Ex

We can derive the derivative of 10x using proofs.

To demonstrate this, we use the rules of differentiation and properties of exponential functions.

Methods include:

Using the Exponential Rule

Using the Chain Rule

Using the Exponential Rule

The derivative of 10x can be shown using the exponential rule for differentiation.

Consider the function f(x) = 10x.

The derivative of an exponential function ax is d/dx (ax) = ax ln(a).

Therefore, for f(x) = 10x, the derivative is: f'(x) = 10x ln(10).

Thus, the derivative of 10x is (10x) ln(10).

Using the Chain Rule

To prove the differentiation of 10x using the chain rule,

Consider f(x) = 10x

Express it as f(x) = e(x ln(10))

Using the chain rule, d/dx [e(g(x))] = e(g(x)) g'(x)

Here, g(x) = x ln(10), so g'(x) = ln(10)

The derivative is: d/dx (e(x ln(10))) = e(x ln(10)) ln(10)

Substitute back: f'(x) = 10x ln(10)

Thus, the derivative of 10x is (10x) ln(10).