Question

Ajudinha em Derivada :
f(X)=(x+√x ) (x-2√x)

Answer 1

$f(x)=u(x)\cdot v(x)\\ \\ f'(x)=u'(x)\cdot v(x)+u(x)\cdot v'(x)\\ \\ f(x)=(x+\sqrt x)(x-2\sqrt x)\\ \\u(x)=x+\sqrt x\\ \\ u'(x)=1+\frac{1}{2\sqrt x}\\ \\ v(x)=x-2\sqrt x\\ \\ v'(x)=1-\frac{1}{\sqrt x}\\ \\ f'(x)=(1+\frac{1}{2\sqrt x})(x-2\sqrt x)+(x+\sqrt x)(1-\frac{1}{\sqrt x})\\ \\ f'(x)=x-2\sqrtx+\frac{x}{2\sqrt x}-1+x-\frac{x}{\sqrt x}+\sqrt x-1\\ \\ f'(x)=2x-4+\frac{\sqrt x}{2}$