Question

$\frac{d\left(\sin \left(2x^2\right)\right)}{dx}$

• A. $4x\cos \left(2x^2\right)$
• B. $2\sin \left(x^2\right)\cos \left(x^2\right)$
• C. $4x\sin \left(x^2\right)$
• D. $4x\sin \left(x^2\right)\cos \left(x^2\right)$

Answer 1

The correct option is A

$4x\cos \left(2x^2\right)$

Explanation for correct option:

Given, $\frac{d\left(\sin \left(2x^2\right)\right)}{dx}$

Differentiate w.r.t $x$.

$\begin{array}{rcl}\frac{d\left(\sin \left(2x^2\right)\right)}{dx}& =& \cos \left(2x^2\right)\times 2\times 2\times x\\ & =& 4x\cos \left(2x^2\right)\\ & \Rightarrow & \frac{d\left(\sin \left(2x^2\right)\right)}{dx}=4x\cos \left(2x^2\right)\end{array}$

Therefore, correct answer is option $\left(A\right)$.