Question

If $A$ is a square matrix with $\left|A\right|=6$ find the value of $\left|AA\prime \right|$ Find the derivation of $\cos \left(\sin x\right)$ w.r.t ${}^{\prime }{x}^{\prime }$

Answer 1

$|A{A}^{\prime }|=|A||A^{\prime }|=|A|\times |A|=6\times 6=36$

Let $y=\cos \left(\sin x\right)$

Differentiating w.r.t. $x$

$\frac{dy}{dx}=-\sin x\left(sinx\right)\times cosx=-\cos xsin\left(sinx\right)$