Question

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

Answer 1

`-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)`