Question

If $y=(10{)}^{(10{)}^{{\log }_{10}cosec\left(10x\right)}}$, find $\frac{dy}{dx}$

Answer 1

Given,

$y=(10{)}^{(10{)}^{{\log }_{10}cosec\left(10x\right)}}$

or, $y=(10{)}^{cosec\left(10x\right)}$. [ ${10}^{{\log }_{10}x}=x$}

Now differentiating both sides we get,

$\frac{dy}{dx}={10}^{cosec\left(10x\right)}.{\log }_{e}10.(-cosec(10x).\cot (10x\left)\right).10$