How do you differentiate f(x)= (4x^2+5)*e^(x^2) using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Henry W. Oct 18, 2016 f'(x)=2xe^(x^2)(4x^2+9) Explanation: Product rule: f'(x)=u'v+v'u f(x)=(4x^2+5)*e^(x^2) Let u=4x^2+5 and v=e^(x^2) u'=8x v'=2xe^(x^2) :.f'(x)=8x*e^(x^2)+2xe^(x^2)*(4x^2+5) =2xe^(x^2)(4+4x^2+5) =2xe^(x^2)(4x^2+9) 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 1746 views around the world You can reuse this answer Creative Commons License