Question

Differentiate the following function w.r.t. x: $\sqrt{log\left\{sin(\frac{x^2}{3}-1)\right\}}$

Answer 1

According to question,

$\begin{array}{c}y=\sqrt{\log \left(\sin \left(\frac{x^2}{3}-1\right)\right)}\\ y^{\prime }=\frac{1}{2\sqrt{\log \left(\sin \left(\frac{x^2}{3}-1\right)\right)}}\cdot \frac{1}{\left(\sin \left(\frac{x^2}{3}-1\right)\right)}\cdot \cos \left(\frac{x^2}{3}-1\right)\times \frac{2x}{3}\\ y^{\prime }=\frac{x}{3}\cdot \frac{\cos \left(\frac{x^2}{3}-1\right)}{\sin \left(\frac{x^2}{3}-1\right)\sqrt{\log \left(\sin \left(\frac{x^2}{3}-1\right)\right)}}\end{array}$