How do you differentiate #f(x)=e^(-6x) sin(3x)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Bio Nov 3, 2015 #f'(x)=3e^{-6x}[cos(3x)-2sin(3x)]# Explanation: #f'(x)=frac{d}{dx}(e^{-6x}sin(3x))# #=e^{-6x}frac{d}{dx}(sin(3x))+sin(3x)frac{d}{dx}(e^{-6x})# #=e^{-6x}(3cos(3x))+sin(3x)(-6e^{-6x})# #=3e^{-6x}[cos(3x)-2sin(3x)]# 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 1508 views around the world You can reuse this answer Creative Commons License