Question

How do you find the derivative of `y = arctan(x^2)`?

Answer 1

`( 2x)/(1 + x^4)`

Explanation:

Using the `color(blue)" chain rule "`

`d/dx [ f(g(x)) ] = f'(g(x)) . g'(x)`

and the standard derivative `d/dx(tan^-1 x) = 1/(1 + x^2)`

`rArr dy/dx = 1/(1 + (x^2)^2) .d/dx (x^2) = (2x)/(1 + x^4)`