# What is the derivative of #arctan(x)^(1/2)#?

##### 1 Answer

Nov 3, 2016

#### Explanation:

I usually make no attempt to remember the derivatives of inverse trig function and would have to look up the result.

Therefore, Inverse trig functions are more easily differentiated by rewriting in terms of the non-inverse trig function and implicit differentiating.

Let

# :. y = sqrt(arctanx) #

# :. y^2=arctanx #

# :. tan(y^2)=x #

If we (implicity) differentiate we get:

Using the trig identity

And so we have:

Hence,