Question

If y=〖tan^(-1) (〗⁡〖(5x-4)/(5+4x)〗) then dy/dx =………..​

Answer 1

Step-by-step explanation:

We have,

$y = \tan^ {- 1} ( \frac{5x - 4}{5 + 4x} )$

Differentiating both sides w.r.t x, we have,

$\frac{dy}{dx} = \frac{1}{1 + (\frac{5x - 4}{5 + 4x})^{2} } \times \frac{5(5 + 4x) - 4(5x - 4)}{(5 + 4x)^{2} }$

$= > \frac{dy}{dx} = \frac{(5 + 4x)^{2} }{ {(5 + 4x)}^{2} + {(5x - 4)}^{2} } \times \frac{25 + 20x - 20x + 16}{ {(5 + 4x)}^{2} }$

$= > \frac{dy}{dx} = \frac{41}{41( {x}^{2} + 1)}$

$= > \frac{dy}{dx} = \frac{1}{ {x}^{2} + 1 }$