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Derivatives & Second-Order Derivatives · Question 9 of 96

Question 9

MediumOriginal question

What is ddx(5x)\frac{d}{dx}\left(5^x\right)?

Options for question 9

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Write 5x=exlog⁡55^x = e^{x \log 5}.

  2. By the chain rule its derivative is exlog⁡5⋅log⁡5=5xlog⁡5e^{x \log 5} \cdot \log 5 = 5^x \log 5.

Worth noting

x⋅5x−1x \cdot 5^{x - 1} treats 5x5^x like a power of xx; here the variable is in the exponent.

Concept
Derivative of an exponential function
Typical time
90 s
Your time
—
The rule this testsThe rules of differentiation
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