What is the derivative of # e^(1/x)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Shwetank Mauria Mar 20, 2016 #d/(dx)e^(1/x)=-e^(1/x)/x^2# Explanation: To find derivative of #e^(1/x)#, we use function of a function i.e. if #f(g(x))#, #(df)/(dx)=(df)/(dg)xx(dg)/(dx)# Hence #d/(dx)e^(1/x)# is equal to #e^(1/x)xxd/(dx)(1/x)=e^(1/x)xx(-1/x^2)=-e^(1/x)/x^2# Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of #y= 6cos(x^2)# ? How do you find the derivative of #y=6 cos(x^3+3)# ? How do you find the derivative of #y=e^(x^2)# ? How do you find the derivative of #y=ln(sin(x))# ? How do you find the derivative of #y=ln(e^x+3)# ? How do you find the derivative of #y=tan(5x)# ? How do you find the derivative of #y= (4x-x^2)^10# ? How do you find the derivative of #y= (x^2+3x+5)^(1/4)# ? How do you find the derivative of #y= ((1+x)/(1-x))^3# ? See all questions in Chain Rule Impact of this question 19826 views around the world You can reuse this answer Creative Commons License