Question

qual a derivada de x^2+√x

Answer 1

Calcular a derivada da função

     $y=x^2+\sqrt{x}\\\\ y=x^2+x^{1/2}$


Aqui devemos usar a regra para derivar potências:

     •   $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$


Derivando a função, obtemos

     $\dfrac{dy}{dx}=\dfrac{d}{dx}(x^2+x^{1/2})\\\\\\ \dfrac{dy}{dx}=\dfrac{d}{dx}(x^2)+\dfrac{d}{dx}(x^{1/2})\\\\\\ \dfrac{dy}{dx}=2x^{2-1}+\dfrac{1}{2}\,x^{(1/2)-1}\\\\\\ \dfrac{dy}{dx}=2x^1+\dfrac{1}{2}\,x^{-1/2}\\\\\\ \dfrac{dy}{dx}=2x+\dfrac{1}{2x^{1/2}}$

     $\dfrac{dy}{dx}=2x+\dfrac{1}{2\sqrt{x}}\quad\longleftarrow\quad\textsf{resposta.}$


Bons estudos! :-)

Answer 2

$\sf{\dfrac{d}{dx}(x^2+\sqrt{x})=2x+\dfrac{1}{2\sqrt{x}}}$