Differentiate the following function with respect of `x :(2^x cot x)/(sqrt(x))`

Explanation

`frac{d}{d x}(frac{2^{x} cot x}{sqrt{x}})`


`=frac{sqrt{x} frac{d}{d x}(2^{x} cdot cot x)-2^{x} cot x(frac{d}{d x} sqrt{x})}{(sqrt{x})^{2}}`


`=frac{sqrt{x}(-2^{x} csc ^{2} x+2^{x} cot x cdot log 2)-frac{2^{x} cot x}{2 sqrt{x}}}{(sqrt{x})^{2}}`


`=frac{2 x(-2^{x} csc ^{2} x+2^{x} cot x cdot log 2)-2^{x} cot x}{2 x sqrt{x}}`


`=frac{2^{x}}{sqrt{x}}(-csc ^{2} x+log 2 cot x-frac{cot x}{2 x})`


`=frac{2^{x}(-2 x csc ^{2} x+2 x cot x log 2-cot x)}{2 x sqrt{x}}`


`=frac{2^{x}}{sqrt{x}}(frac{-2 x csc ^{2} x}{2 x}+frac{2 x cot x log 2}{2 x}-frac{cot x}{2 x})`