How do you find the derivative of #f(x) = e^x + e^(-x / 2)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Trevor Ryan. Feb 3, 2016 #f'(x)=e^x-1/(2e^x)# Explanation: Rule : #d/dx e^(u(x))=e^u*(du)/dx#. Application thereof : #d/dx[e^x+e^(-x/2)]=e^x-1/2e^(-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 1153 views around the world You can reuse this answer Creative Commons License