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Chain Rule, Log Differentiation & Rate of Change · Question 55 of 130

Question 55

EasyOriginal question

If f(x)=log⁡(x2+1)f(x) = \log{\left(x^{2} + 1 \right)}, what is f′(1)f'\left(1\right)?

Options for question 55

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. f′(x)=2x1+x2f'(x) = \frac{2x}{1 + x^{2}}.

  2. At 1: 22=1\frac{2}{2} = 1.

Worth noting

log⁡2\log 2 is f(1)f(1) itself, the value, not the slope.

Concept
A logarithmic derivative at a point
Typical time
60 s
Your time
—
The rule this testsExponential and logarithmic functions
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.