What is the derivative of $x * ((4-x^2)^(1/2))$ ?

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Answer 1 · 2017-12-14T22:55:09

$-(2*(-2+x^2))/sqrt(4-x^2)$

$f'(a*b)=b*f'(a)+a*f'(b)$

Let $color(white)(88)a=x$

Let $color(white)(88)b=(4-x^2)^(1/2)$

$f'(a)=1$

$f'(b)=1/2(4-x^2)^(-1/2)*-2x=-x(4-x^2)^(-1/2)$

$f'(a*b)=(4-x^2)^(1/2) * 1+x * -x(4-x^2)^(-1/2)$

$->=(4-x^2)^(1/2)+(-x^2)/(4-x^2)^(1/2)=-(2*(-2+x^2))/sqrt(4-x^2)$

What is the derivative of x * ((4-x^2)^(1/2))x * ((4-x^2)^(1/2))?