Question

Cat este (e la puterea 1/x) derivat?

Answer 1

$\left(e^{\frac{1}x}\right)'=e^{\frac{1}x}\cdot\left(\dfrac{1}x\right)'=-\dfrac{e^{\frac{1}x}}{x^2}\\\\ Am folosit formula\ (x^n)'=n\cdot x^{n-1},\ adic\breve{a}\ (x^{-1})'=-1\cdot x^{-2}=-\dfrac{1}{x^2}.$

Simplu, nu ?

Green eyes.

Answer 2

$\Big({e^{\dfrac{1}{x}}}\Big) ' = e^{\dfrac{1}{x}}\cdot \Big(\dfrac{1}{x}\Big)' = e^\dfrac{1}{x} }\cdot (x^{-1})'= e^\dfrac{1}{x} }\cdot (-1\cdot x^{-1-1})= e^\dfrac{1}{x} }\cdot(- x^{-2})= \\ \\ =e^\dfrac{1}{x}} \cdot\Big(-\dfrac{1}{x^2}\Big)= -\dfrac{e^\dfrac{1}{x}}{x^2} \\ \\ \\ M-am folosit de formulele: \left\| \begin{array}{c} (e^u)' = e^u\cdot u' \\ (x^n)' = n\cdotx^{n-1} \end{array} \right$