How do you differentiate f(x)=(5e^x+cosx)(x-2) using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Gerardina C. Feb 10, 2017 =5xe^x-5e^x-xsinx+2sinx+cosx Explanation: If f(x)=g(x)*h(x), you know that f'(x)=g'(x)*h(x)+g(x)*h'(x) (product rule), then f'(x)=(5e^x-sinx)(x-2)+(5e^x+cosx)*1 =5xe^x-xsinx-10e^x+2sinx+5e^x+cosx =5xe^x-5e^x-xsinx+2sinx+cosx 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 1759 views around the world You can reuse this answer Creative Commons License