How do you differentiate #f(x) =x sqrt(4-x^2) # using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer S S. Feb 15, 2018 #-x^2/sqrt(4-x^2)+sqrt(4-x^2) # Explanation: #d/dx(xsqrt(4-x^2) )=xd/dx(sqrt(4-x^2 ))+d/dx(x)sqrt(4-x^2)=x(1/2(4-x^2)^(-1/2)(-2x)+1sqrt(4-x^2)=-x^2/sqrt(4-x^2)+sqrt(4-x^2)# 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 1558 views around the world You can reuse this answer Creative Commons License