Question

Alguém pode mim salvar aqui e derivar por favor f(x)=(√x+3)(x²+6)

Answer 1

Dado:
$f(x)=(3+\sqrt{x})(x^2+8)$

Sabendo que:
$\frac{d}{dx}(3+ \sqrt{x} )= \frac{1}{2} . \frac{1}{x^2}$

E que:
$\frac{d}{dx}(x^2+6 )= 2x$

Podemos aplicar a regra:
$f'(x)=u'v+uv'$
$f'(x)=\frac{1}{2} . \frac{1}{x^2}.(x^2+6)+(\sqrt{x}+3).2x\\\\ f'(x)=\frac{x^2+6}{2x^2}+2x^{3/2}+6x\\\\ f'(x)=\frac{x^2+6+2x^{7/2}+12x^3}{2x^2}\\\\ f'(x)= \frac{12x^3}{2x^2}+ \frac{2x^{7/2}}{2x^2} +\frac{x^2}{2x^2}+\frac{6}{2x^2}\\\\ f'(x)=6x+x^{3/2}+\frac{1}{2}+\frac{3}{x^2}$

Ik_Lob