Differentiate `tan^(-1){(2^(x+1))/(1-4^x)},\ -oo

Explanation

Solution:

`{lan}^{-1}(\frac{2 {lan} \theta}{1-\tan ^{2} \theta}\right) { because, 2^{-\infty}<2^{x}<2^{0}} `

`={lan}^{-1}({lan} 2 \theta) {because, 0<2^{x}<1 }`

=` 0<{lan} \theta<1 `

`y=2 {lan}^{-1} 2^{x} 0<\theta<\pi / 4 `

`d y / d x=\frac{2 \cdot 1}{1+(2^{x}\right)^{2}} \cdot 2^{x} \ln 2 0<2 \theta<\pi / 2 `

` =\frac{2^{x+1} \ln 2}{1+4^{x}}`