How do you differentiate f(x) =x sqrt(4-x^2) f(x)=x√4−x2 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) −x2√4−x2+√4−x2 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)ddx(x√4−x2)=xddx(√4−x2)+ddx(x)√4−x2=x(12(4−x2)−12(−2x)+1√4−x2=−x2√4−x2+√4−x2 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)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)y=x2⋅sin(x) ? How do you use the product rule to differentiate y=cos(x)*sin(x)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)f(x)=(x4+x)⋅ex⋅tan(x) ? How do you use the product rule to find the derivative of y=(x^3+2x)*e^xy=(x3+2x)⋅ex ? How do you use the product rule to find the derivative of y=sqrt(x)*cos(x)y=√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)y=(1x2−3x4)⋅(x+5x3) ? How do you use the product rule to find the derivative of y=sqrt(x)*e^xy=√x⋅ex ? How do you use the product rule to find the derivative of y=x*ln(x)y=x⋅ln(x) ? See all questions in Product Rule Impact of this question 1730 views around the world You can reuse this answer Creative Commons License