Match List-I with List-II
| List-I | List-II | ||
| (A) | $\frac{d}{dx}(sin\, x^2)$ | (I) | $\frac{1}{5}$ |
| (B) | $\frac{d}{dx}(e^{sin\, x})$ | (II) | 0 |
| (C) | $f(x)=tan^{-1}x$ then $f'(2)$ | (III) | $2xcosx^2$ |
| (D) | If $y=3 \, cos x-2 \, sin x , $ then $\frac{d^2y}{dx^2}+y$ | (IV) | $e^{sinx}.cosx$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 3
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)