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Chain Rule, Log Differentiation & Rate of Change · Question 68 of 130

Match each function in List I, for x > 0, with its derivative in List II.

Question 68

MediumOriginal question

Match each function in List I, for x>0x > 0, with its derivative in List II.

List IList II
A. log⁡x3\log x^{3}I. 3e3x3e^{3x}
B. (log⁡x)3(\log x)^{3}II. 3x\frac{3}{x}
C. e3xe^{3x}III. 3xlog⁡33^{x}\log 3
D. 3x3^{x}IV. 3(log⁡x)2x\frac{3(\log x)^{2}}{x}
Options for question 68

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. A: log⁡x3=3log⁡x\log x^{3} = 3\log x, derivative 3x\frac{3}{x}. B: chain rule, 3(log⁡x)2⋅1x3(\log x)^{2} \cdot \frac{1}{x}.

  2. C: e3x⋅3e^{3x} \cdot 3. D: a constant base, so 3xlog⁡33^{x}\log 3.

Worth noting

log⁡x3\log x^{3} cubes xx inside the logarithm; (log⁡x)3(\log x)^{3} cubes the logarithm itself.

Concept
Telling look-alike exponentials and logarithms apart
Typical time
120 s
Your time
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The rule this testsExponential and logarithmic functions
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