Question

Determine a derivada de primeira ordem para a seguinte função:
Y=Raiz quarta de x elevado a 5
Me ajudem pfv

Answer 1

$\dfrac{dy(x)}{dx}~=~\left(\sqrt[4]{x}^{\,5}\right)'\\\\\\\dfrac{dy(x)}{dx}~=~\left(\left(x^{\frac{1}{4}}\right)^5\right)'\\\\\\\dfrac{dy(x)}{dx}~=~\left(x^{\frac{5}{4}}\right)'\\\\\\\dfrac{dy(x)}{dx}~=~\dfrac{5}{4}\,.\,x^{\frac{5}{4}-1}\\\\\\\dfrac{dy(x)}{dx}~=~\dfrac{5}{4}\,.\,x^{\frac{1}{4}}\\\\\\\boxed{\dfrac{dy(x)}{dx}~=~\dfrac{5\sqrt[4]{x}}{4}}$

Answer 2

Resposta:

y= $5\frac{1}{\sqrt[5]{x^{4} } }$

Explicação passo a passo:

y=$\sqrt[5]{x}$

y=$x^{1/2-1}$

y=$\frac{1}{5}$ X $x^{1/5-5/5}$

y=$\frac{1}{5}.\frac{-4}{5}$

y=$\frac{1}{5} . (\frac{1}{x} )^{-4/5}$

y=$\frac{1}{5} .\frac{1}{x^{4/5} }$

y= $5\frac{1}{\sqrt[5]{x^{4} } }$

respondi e acertei espero ter ajudado.