# How do you take the derivative of #tan^-1(x^2)#?

##### 1 Answer

Aug 26, 2015

#### Explanation:

You can differentiate a function

So, if you have a function

#tan(y) = x^2#

Differentiate both sides with respect to

#d/(dy)(tany) * (dy)/dx = d/dx(x^2)#

#sec^2y * (dy)/dx = 2x#

This is equivalent to saying that

#(dy)/dx = (2x)/sec^2y#

Remember that you have

#color(blue)(sec^2x = 1 + tan^2x)#

which means that you get

#(dy)/dx = (2x)/(1 + tan^2y)#

Finally, replace

#(dy)/dx = color(green)((2x)/(1 + x^4))#