Question

Find the derivative of $x^2+x\left(sinx\right)$ ?

• A. 2x + x cos x + sin x
• B. $x^2$ sin x + cosx
• C. 2x + cos x + sin x
• D. none of these

Answer 1

The correct option is A

2x + x cos x + sin x

$\frac{d(x^2+x(sinx\left)\right)}{dx}=\frac{d\left(x^2\right)}{dx}+\frac{d\left(xsinx\right)}{dx}$
=$2x+x\frac{d\left(sinx\right)}{dx}+sinx\frac{dx}{dx}$(using product rule)
=2x + x cosx + sinx