Question

Cat este derivata lui : 4 pe radical din x ?

Answer 1

$\left(\dfrac{4}{\sqrt x}\right)^{'}=(4\cdot x^{-\frac{1}2})^{'}=4\cdot\left(-\dfrac{1}{2}\right)\cdot x^{-\frac{1}2-1}=-2\cdot x^{-\frac{3}2}=-\dfrac{2}{\sqrt{x^3}}=-\dfrac{2}{x\cdot\sqrt x}.$

A doua soluţie:

$\left(\dfrac{4}{\sqrt x}\right)^{'}=\dfrac{4^{'}\cdot\sqrt x-4\cdot(\sqrt x)^{'}}{(\sqrt x)^2}=\dfrac{0\cdot\sqrt x-4\cdot\dfrac{1}{2\sqrt x}}{x}=-\dfrac{2}{x\cdot\sqrt x}.$

Green eyes.