Question

знайти похідну f(x)=1/(3+√х)​

Answer 1

Ответ:

$\displaystyle f(x)=\frac{1}{3+\sqrt{x}}\ \ ,\\\\\\\Big(\frac{1}{v}\Big)'=-\frac{v'}{v^2}\ \ ,\ \ v=3+\sqrt{x}\\\\(\sqrt{x})'=\frac{1}{2\sqrt{x}}\\\\\\f'(x)=-\frac{(3+\sqrt{x})'}{(\, 3+\sqrt{x}\ )^2}=-\frac{\dfrac{1}{2\sqrt{x}}}{(3+\sqrt{x})^2}=-\frac{1}{2\sqrt{x}\cdot (3+\sqrt{x})^2}$  

$P.S.\ \ \Big(\dfrac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}\ \ \ \Rightarrow \ \ \ \Big(\dfrac{1}{v}\Big)'=\dfrac{0\cdot v-1\cdot v'}{v^2}=-\dfrac{v'}{v^2}$