# How do you use the chain rule to differentiate #y=(x^2+1)^(1/2)#?

##### 2 Answers

Feb 26, 2017

#### Explanation:

Apply the power rule and the chain rule:

Apply the power rule:

Recall that the chain rule is similar as the power rule but has one more step.

#### Explanation:

The chain rule states that the derivative of

In this instance,

#f(x) = g(x)^(1/2)#

#g(x) = x^2 + 1 #

So, the derivative of the composition

#(1/2) * (x^2 + 1)^(-1/2) * 2x#

Simplified, we get:

#x / sqrt(x^2 + 1)#