Question

If $S=e^x-\sin x$, find $\frac{d^{2}S}{d{x}^2}$

• A. $e^x+\cos x$
• B. $e^x-\sin x$
• C. $e^x+\sin x$
• D. $e^x-\cos x$

Answer 1

The correct option is C $e^x+\sin x$

Given, $S=e^x-\sin x$
$\frac{d^{2}S}{d{x}^2}\Rightarrow \frac{d\left(\frac{dS}{dx}\right)}{dx}$
So, we have $\frac{dS}{dx}=\frac{d(e^x-\sin x)}{dx}$
$\Rightarrow \frac{d{e}^x}{dx}-\frac{d\sin x}{dx}=e^x-\cos x$
Thus, $\frac{d^{2}S}{d{x}^2}=\frac{d(e^x-\cos x)}{dx}$
$\Rightarrow \frac{d{e}^x}{dx}-\frac{d\cos x}{dx}=e^x+\sin x$