Question

If $x\cdot e^{xy}=y+{\sin }^{2}x$, then at $x=0$, $\frac{dy}{dx}=$?

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

Answer: (A)

$1$

Given

$x\cdot e^{xy}=y+{\sin }^{2}x$

Differentiate on both sides

$e^{xy}+x\cdot e^{xy}(1+\frac{dy}{dx})=\frac{dy}{dx}+2\sin x\cdot \cos x$

at $x=0$

$1+0\times e^{0\cdot y}(1+\frac{dy}{dx})=\frac{dy}{dx}+0$

$\frac{dy}{dx}=1$.