How do you differentiate #f(x)=e^x*sinx# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Steve M Oct 20, 2016 # f'(x) = e^xcosx + e^xsinx # Explanation: Use the product rule #d/dx(uv)=u(dv)/dx + v(du)/dx# So, with #f(x)=e^xsinx# we have: # f'(x) = e^xd/dxsinx+ sinxd/dxe^x # # :. f'(x) = e^xcosx+ sinxe^x # # :. f'(x) = e^xcosx + e^xsinx # Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x - 3)(2 - 3x)(5 - x)# ? How do you use the product rule to find the derivative of #y=x^2*sin(x)# ? How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x^4 +x)*e^x*tan(x)# ? How do you use the product rule to find the derivative of #y=(x^3+2x)*e^x# ? How do you use the product rule to find the derivative of #y=sqrt(x)*cos(x)# ? How do you use the product rule to find the derivative of #y=(1/x^2-3/x^4)*(x+5x^3)# ? How do you use the product rule to find the derivative of #y=sqrt(x)*e^x# ? How do you use the product rule to find the derivative of #y=x*ln(x)# ? See all questions in Product Rule Impact of this question 5827 views around the world You can reuse this answer Creative Commons License