Question

Derivada de f(x)= x^1/2+x^1/3-x^1/4

Answer 1

Olá.

Basta aplicar as seguintes propriedades:

$\star ~y = u + v\Rightarrow y' = u' + v'\\ \\ \\ \star ~y= x^n\Rightarrow y' = n\cdot x^{n-1}$

Vamos lá:

$y = x^{\frac12} + x^{\frac13}+x^{\frac14}\\ \\ y' = \frac12 x^{-\frac12} + \frac13 x^{-\frac23} + \frac14 x ^{-\frac34}\\ \\ \\ \boxed{y' = f'(x) = \dfrac{1}{2\sqrt x} + \dfrac{1}{ 3\sqrt[3]{x^2} } + \dfrac{1}{4\sqrt[4]{x^3}}}$