Which of the following statements are true? I. d/dxsin^-1 x + d/dxcos^-1 x = 0 for | x | 1.

Question 35

MediumOriginal question

Which of the following statements are true?
I. $\frac{d}{dx}\sin^{-1} x + \frac{d}{dx}\cos^{-1} x = 0$ for $\lvert x \rvert < 1$ .
II. $\frac{d}{dx}\tan^{-1} x = \sec^{2} x$ .
III. $\frac{d}{dx}\cot^{-1} x = -\frac{1}{1 + x^{2}}$ .
IV. $\frac{d}{dx}\sec^{-1} x = \frac{1}{x\sqrt{x^{2} - 1}}$ for $x > 1$ .

All four: I, II, III and IVCorrect answerYour answerIII and IV onlyCorrect answerYour answerI, III and IV onlyCorrect answerYour answerI and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

I: $\frac{1}{\sqrt{1 - x^{2}}} - \frac{1}{\sqrt{1 - x^{2}}} = 0$ . III and IV are the standard results.
II is false: $\sec^{2} x$ is the derivative of $\tan x$ ; $\tan^{-1} x$ gives $\frac{1}{1 + x^{2}}$ .

Worth noting

II confuses the inverse function with the reciprocal of $\tan$ 's derivative.

Concept: The standard inverse trigonometric derivatives
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsDerivatives of inverse trigonometric functions

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