Question:

Match List I with List II
List I
(Functions) List II
(Derivatives)
A. f(x)=sin^-1x I. \(\frac{1}{1+x^2}\), x ∈ R
B. f(x)=tan^-1x II. \(\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
C. f(x)=cos^-1x III. \(-\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
D. f(x)=sin^-1x IV. \(-\frac{1}{1+x^2}\), x ∈ R
Choose the correct answer from the options given below :

Updated On: Jun 13, 2024

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The Correct Option is C

The correct option is (C) :A-II, B-I, C-III, D-IV.

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List-I	List-II
The derivative of \( \log_e x \) with respect to \( \frac{1}{x} \) at \( x = 5 \) is	(I) -5
If \( x^3 + x^2y + xy^2 - 21x = 0 \), then \( \frac{dy}{dx} \) at \( (1, 1) \) is	(II) -6
If \( f(x) = x^3 \log_e \frac{1}{x} \), then \( f'(1) + f''(1) \) is	(III) 5
If \( y = f(x^2) \) and \( f'(x) = e^{\sqrt{x}} \), then \( \frac{dy}{dx} \) at \( x = 0 \) is	(IV) 0