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Chain Rule, Log Differentiation & Rate of Change · Question 101 of 130

Question 101

HardOriginal question

If f(x)=xxf(x) = x^{x}, what is f′(2)f'\left(2\right)?

Options for question 101

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. f′(x)=xx(1+log⁡x)f'(x) = x^{x}(1 + \log x).

  2. At 2: 4(1+log⁡2)4(1 + \log 2).

Worth noting

4 is f(2)=22f(2) = 2^{2}, before the factor 1+log⁡21 + \log 2.

Concept
Logarithmic differentiation at a point
Typical time
120 s
Your time
—
The rule this testsLogarithmic differentiation
Practise this chapter →

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Practise this chapter →

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.