What is the derivative of #e^(-x)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer georgef Jul 9, 2016 You have to use the chain rule Explanation: To evaluate the #(e^-x)'# you must calculate the #(e^u)' * u'#, where #u=-x#. But, #(e^u)' = e^u#, and #u'=-1#, and then: #(e^-x)'=e^-x * (-1)= -e^-x# 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 1517 views around the world You can reuse this answer Creative Commons License