How do you differentiate f(x) =x sqrt(4-x^2) f(x)=x4x2 using the product rule?

1 Answer
Feb 15, 2018

-x^2/sqrt(4-x^2)+sqrt(4-x^2) x24x2+4x2

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(x4x2)=xddx(4x2)+ddx(x)4x2=x(12(4x2)12(2x)+14x2=x24x2+4x2