Question

Assertion (A) $\frac{d}{d x} e^{\cos x}=e^{\cos x}(-\sin x)$
Reason (R) $\frac{d}{d x} e^x=e^x$

• A. Both A and R are correct; R is the correct explanation of A
• B. Both A and R are correct; R is not the correct explanation of A
• C. A is correct; R is incorrect
• D. R is correct; A is incorrect

Answer 1

Answer: (B)

Let $y=e^{\cos x}$. Using chain rule, we have
$\frac{d y}{d x}=e^{\cos x} \cdot(-\sin x)=(-\sin x)=-(\sin x) e^{\cos x}$
Also, $\frac{d}{d x}\left(e^x\right)=e^x$