How do you use the chain rule to differentiate #f(x)=e^(3x)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Alan N. Aug 27, 2016 #f'(x)=3e^(3x)# Explanation: If #f(x) = f(g(x))# then the Chain rule states that: #f'(x) = f'(g(x))*g'(x))# In this example: #f(x) = e^(g(x))# and #g(x) = 3x# #:. f'(x) = e^(3x) * d/dx(3x) = e^(3x) * 3# #= 3e^(3x)# 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 900 views around the world You can reuse this answer Creative Commons License