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Original
2026-01-01
Modified
2026-02-28
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<p>We can derive the derivative of 10x using proofs.</p>
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<p>We can derive the derivative of 10x using proofs.</p>
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<p>To demonstrate this, we use the rules of differentiation and properties of exponential functions.</p>
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<p>To demonstrate this, we use the rules of differentiation and properties of exponential functions.</p>
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<p>Methods include:</p>
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<p>Methods include:</p>
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<p>Using the Exponential Rule</p>
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<p>Using the Exponential Rule</p>
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<p>Using the Chain Rule</p>
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<p>Using the Chain Rule</p>
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<p>Using the Exponential Rule</p>
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<p>Using the Exponential Rule</p>
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<p>The derivative of 10x can be shown using the exponential rule for differentiation.</p>
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<p>The derivative of 10x can be shown using the exponential rule for differentiation.</p>
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<p>Consider the function f(x) = 10x.</p>
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<p>Consider the function f(x) = 10x.</p>
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<p>The derivative of an exponential function ax is d/dx (ax) = ax ln(a).</p>
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<p>The derivative of an exponential function ax is d/dx (ax) = ax ln(a).</p>
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<p>Therefore, for f(x) = 10x, the derivative is: f'(x) = 10x ln(10).</p>
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<p>Therefore, for f(x) = 10x, the derivative is: f'(x) = 10x ln(10).</p>
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<p>Thus, the derivative of 10x is (10x) ln(10).</p>
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<p>Thus, the derivative of 10x is (10x) ln(10).</p>
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<p>Using the Chain Rule</p>
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<p>Using the Chain Rule</p>
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<p>To prove the differentiation of 10x using the chain rule,</p>
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<p>To prove the differentiation of 10x using the chain rule,</p>
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<p>Consider f(x) = 10x</p>
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<p>Consider f(x) = 10x</p>
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<p>Express it as f(x) = e(x ln(10))</p>
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<p>Express it as f(x) = e(x ln(10))</p>
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<p>Using the chain rule, d/dx [e(g(x))] = e(g(x)) g'(x)</p>
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<p>Using the chain rule, d/dx [e(g(x))] = e(g(x)) g'(x)</p>
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<p>Here, g(x) = x ln(10), so g'(x) = ln(10)</p>
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<p>Here, g(x) = x ln(10), so g'(x) = ln(10)</p>
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<p>The derivative is: d/dx (e(x ln(10))) = e(x ln(10)) ln(10)</p>
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<p>The derivative is: d/dx (e(x ln(10))) = e(x ln(10)) ln(10)</p>
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<p>Substitute back: f'(x) = 10x ln(10)</p>
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<p>Substitute back: f'(x) = 10x ln(10)</p>
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<p>Thus, the derivative of 10x is (10x) ln(10).</p>
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<p>Thus, the derivative of 10x is (10x) ln(10).</p>
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