Question

If y = cos $x^3.{\sin }^2\left(x^5\right),$ Find $\frac{dy}{dx}$

Answer 1

$\begin{array}{c}y=\cos x^3{\sin }^2\left(x^5\right)\\ Now,\\ \frac{dy}{dx}=2\cos \left(x^3\right)\sin \left(x^5\right)\cos \left(x^5\right)\left(5x^4\right)+\left(-\sin \left(x^3\right){\sin }^2\left(x^5\right)\times 3x^2\right)\\ =10x^4\cos \left(x^3\right)\cos \left(x^5\right)\sin \left(x^5\right)-3x^2\sin \left(x^3\right){\sin }^2\left(x^5\right)\end{array}$

Hence, this is the answer.