How do you differentiate f(x)=(lnx+x)(1+e^x)f(x)=(lnx+x)(1+ex) using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Guilherme N. Jan 5, 2016 Product rule: (ab)'=a'b+ab' Explanation: (df(x))/(dx)=(1/x+1)(1+e^x)+(lnx+x)(e^x) (df(x))/(dx)=(e^x/x+e^x+1/x+1)+(e^xlnx+xe^x) (df(x))/(dx)=e^x(1+1/x+lnx+x)+1/x+1 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 1586 views around the world You can reuse this answer Creative Commons License