Match List-I with List-II

Choose the correct answer from the options given below :

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

The correct answer is Option (3) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(A) $\frac{d}{dx}(\sin\, x^2)=2x\cos x^2$ (III)

(B) $\frac{d}{dx}(e^{\sin x})=\cos e^{\sin x}$ (IV)

(C) $f(x)=\tan^{-1}x$

so $f'(x)=\frac{1}{1+x^2}⇒f'(2)=\frac{1}{5}$ (I)

(D) $y=3\cos x-2\sin x$

$\frac{dy}{dx}=-3\sin x-2\cos x$

$\frac{d^2y}{dx^2}=-3\cos x+2\sin x⇒\frac{d^2y}{dx^2}+y=0$ (II)