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Chain Rule, Log Differentiation & Rate of Change · Question 30 of 130

Question 30

EasyOriginal question

If f(x)=tan⁡−1(x)f(x) = \tan^{-1}{\left(x \right)}, what is f′(1)f'\left(1\right)?

Options for question 30

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. ddxtan⁡−1x=11+x2\frac{d}{dx}\tan^{-1} x = \frac{1}{1 + x^{2}}.

  2. At x=1x = 1: 12\frac{1}{2}.

Worth noting

π4\frac{\pi}{4} is tan⁡−11\tan^{-1} 1 itself, the function's value, not its slope.

Concept
An inverse trigonometric derivative at a point
Typical time
60 s
Your time
—
The rule this testsDerivatives of inverse trigonometric functions
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