Question

Derivative of $f\left(x\right)=\sin (x^3+2x+1)$ is

• A. $\cos (3x^2+2)$
• B. $\cos (x^3+2x+1)(3x^2+2)$
• C. $\cos (x^3+2x+1)(3x^2-2)$
• D. $\cos (x^3+2x+1)$

Answer 1

The correct option is B $\cos (x^3+2x+1)(3x^2+2)$

Given, $f\left(x\right)=\sin (x^3+2x+1)$
So, the derivative of the function is
$\frac{df\left(x\right)}{dx}=\frac{d\left(\sin \right(x^3+2x+1\left)\right)}{dx}$
Using chain rule we have
$\frac{d\left(\sin \right(x^3+2x+1\left)\right)}{d(x^3+2x+1)}\times \frac{d(x^3+2x+1)}{dx}$
$\Rightarrow \frac{d\left(\sin \right(x^3+2x+1\left)\right)}{d(x^3+2x+1)}\times [\frac{d{x}^3}{dx}+2\frac{dx}{dx}+\frac{d1}{dx}]$
$\Rightarrow \cos (x^3+2x+1)(3x^2+2)$