Question #209a9 Calculus Basic Differentiation Rules Chain Rule 1 Answer Douglas K. Mar 24, 2017 Use the product rule : #dy/dx= (f(x)g(x))'=f'(x)g(x)+f(x)g'(x)# Explanation: Use the product rule : #dy/dx= (f(x)g(x))'=f'(x)g(x)+f(x)g'(x)# let #f(x) = e^(3x) and g(x) = sin(4x)#, then it follows that #f'(x) = 3e^(3x) and g'(x)=4cos(4x)# #dy/dx=(3e^(3x))(sin(4x))+(e^(3x))(4cos(4x))# 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 1475 views around the world You can reuse this answer Creative Commons License