Question

Derivative of $f\left(x\right)=\cos \left(x^2\right)$ is

• A. $-\left(2x\right)\sin \left(x^2\right)$
• B. $\left(2x\right)\sin \left(x^2\right)$
• C. $-\left(x^2\right)\sin \left(x^2\right)$
• D. $\left(x^2\right)\sin \left(x^2\right)$

Answer 1

The correct option is A $-\left(2x\right)\sin \left(x^2\right)$

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