Question

How do you use the product rule to find the derivative of y=x√⋅cos(x)y=sqrt(x)*cos(x) ?

Answer 1

$y=\sqrt x\cos x\\ y'=(\sqrt x)'\cos x+\sqrt x (\cos x)'\\ y'=\frac{1}{2\sqrt x}\cos x+\sqrt x\cdot(-\sin x)\\ y'=\frac{1}{2\sqrt x}\cos x-\sqrt x\sin x$