Question

If y=tan^-1(2^(x+1)/1-4^x).find dy/dx

Answer 1

Answer:

$y = {tan}^{ - 1} ( \frac{2. {2}^{x} }{1 - { ({2}^{x} )}^{2} } ) \\ \\ y = 2 {tan}^{ - 1}( {2}^{x} ) \\ \\ = > \frac{dy}{dx} = 2 \times \frac{1}{1 + {4}^{x} } \times {2}^{x} \times ln(2) \\ \\ = > \frac{dy}{dx} = \frac{ {2}^{(x + 1)} . ln(2) }{1 + {4}^{x} }$