How do you use the chain rule to differentiate y = e^lnx?

2 Answers
Aug 22, 2016

dy/dx = e^lnx/x = 1

Explanation:

Let y = e^u and u = lnx

Then y' = e^u xx 1/x = e^lnx xx 1/x = e^lnx/x = 1

Hopefully this helps!

Aug 22, 2016

f'(x) =1

Explanation:

f(x) = e^lnx = x

f'(x) = d/dx (x) = 1 (No need of the Chain rule)

However, since the question askes that we use the Chain rule:

f(x) = e^lnx
f'(x) = e^lnx * 1/x (Standard differentials and Chain rule)

= x*1/x = 1