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

2 Answers
Oct 15, 2017

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

Explanation:

Use the chain rule by posing #u = 1/x#, so that #y=e^u#:

#dy/dx = dy/(du) (du)/dx = d/(du) e^u xx d/dx 1/x = e^u xx -1/x^2 =-e^(1/x)/x^2#

Oct 15, 2017

Let's see.

Explanation:

Let the equation #y=e^(1/x)# be a function of #x# such that #rarr#

#y=f(x)=e^(1/x)#

Now, differentiating the equation w.r.t #x# we get #rarr#

#dy/dx=d/dx(e^(1/x))#

#:.dy/dx=e^(1/x)cdotd/dx(1/x)# #larr# Chain Rule.

#:.dy/dx=e^(1/x)cdot(-1/x^2)#

#:.color(red)(dy/dx=-e^(1/x)/x^2)#. (Answer).

Hope it Helps:)