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

1 Answer
Jun 23, 2016

Answer:

#(-e^(1/x))/x^2#

Explanation:

Since the derivative of #e^x# is just #e^x#, application of the chain rule to a composite function with #e^x# as the outside function means that:

#d/dx(e^f(x))=e^f(x)*f'(x)#

So, since the power of #e# is #1/x#, we will multiply #e^(1/x)# by the derivative of #1/x#.

Since #1/x=x^-1#, its derivative is #-x^-2=-1/x^2#.

Thus,

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