Question

Differentiate  
log (1 + x²) w.r.t. tan^-1 (x)

Answer 1

Let u = log(1 + x²) and v = tan^-1 (x)

Deffrentiating both sides with respect to x.

`(du)/dx = 1/(1 + x^2) . 2x, (dv)/dx = 1/(1 + x^2)`

`(du)/(dv) = ((du)/dx)/((dv)/dx) = ((2x/1 + x^2))/((1/(1 + x^2))`

`(du)/(dv) = 2x`