How do you find the derivative of # y=e^(x^(1/2))#?

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Answer 1 · 2018-03-09T02:21:07

#e^sqrt(x)/(2sqrt(x))#

A substitution here would help tremendously!

Let's say that #x^(1/2) = u#

now,

#y = e^u#

We know that the derivative of #e^x# is #e^x# so;

#dy/dx = e^u * (du)/dx# using the chain rule

#d/dx x^(1/2) = (du)/dx = 1/2*x^(-1/2) = 1/(2sqrt(x))#

Now plug #(du)/dx# and #u# back into the equation :D

#dy/dx = e^sqrt(x)/(2sqrt(x))#