Question

If $y=e^{\left(x^2+2\sin x\right)},then\frac{dy}{dx}is$

• A. $e^{\left(x^2-2\sin x\right)}$
• B. $e^{\left(x^2+2\sin x\right)}\times \left(2x+2\sin x\right)$
• C. $e^{(x^2+2\sin x)}\times (2x+2\cos x)$
• D. $e^x$

Answer 1

The correct option is B $e^{\left(x^2+2\sin x\right)}\times \left(2x+2\sin x\right)$

Applying log on both sides

$logy=(x^2+2sinx)loge$
$logy=x^2+2sinx$

Differentiating both sides wrt x

$\frac{1}{y}\frac{dy}{dx}=2x+2cosx$

$\frac{dy}{dx}=e^{x^2+2sinx}(2x+2sinx)$