Question

If $S=4x^2-\sin x$, find $\frac{d^{2}S}{d{x}^2}$

• A. $8x-\sin x$
• B. $8x+\sin x$
• C. $8-\sin x$
• D. $8+\sin x$

Answer 1

The correct option is D $8+\sin x$

Given, $S=4x^2-\sin x$
$\frac{d^{2}S}{d{x}^2}\Rightarrow \frac{d\left(\frac{dS}{dx}\right)}{dx}$
So, we have $\frac{dS}{dx}=\frac{d(4x^2-\sin x)}{dx}$
$\Rightarrow 4\frac{d{x}^2}{dx}-\frac{d\sin x}{dx}=8x-\cos x$
Thus, $\frac{d^{2}S}{d{x}^2}=\frac{d(8x-\cos x)}{dx}$
$\Rightarrow 8\frac{dx}{dx}-\frac{d\cos x}{dx}=8+\sin x$