How do you differentiate #g(x) =x^2 sqrt(4+x)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Leland Adriano Alejandro Jan 17, 2016 #g' (x)=(5x^2+16x)/(2 sqrt(x+4)# Explanation: Use the formula #d/dx(u v)= u (dv)/dx + v(du)/dx# Given #g(x)=x^2 sqrt(4+x)# #g' (x)= x^2*1/(2 sqrt(4+x)) *1+sqrt(4+x)*2x# #g' (x)=x^2/(2 sqrt(x+4))+2x* sqrt(x+4)*(2 sqrt(x+4))/(2 sqrt(x+4))# #g' (x)=(x^2+4x^2+16x)/(2 sqrt(x+4))# #g' (x)=(5x^2+16x)/(2 sqrt(x+4)# 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 1197 views around the world You can reuse this answer Creative Commons License