Question

Find `dy/dx if y = tan^-1 ((6x)/[ 1 - 5x^2])`

Answer 1

Let `y = tan^-1 ((6x)/[ 1 - 5x^2])`

 = `tan^-1 ((x +5x) /[ 1 - 5x^2])`
y = `tan^-1 (x) + tan^-1(5x)`
Differentiating w.r.t.x.

`dy/dx = 1/(1 + x^2) + 1/( 1 + 25x^2) xx 5`

= `1/(1 + x^2) + 5/( 1 + 25x^2)`