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)#