Question

calcule a derivada
g(x)=x⁴- ⁴√x³

Answer 1

g'(x) = 4x³ - [(3x²)/4*(x³)^(3/4)]

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30/03/2016
Sepauto - SSRC
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Answer 2

$Fun\c{c}\~ao:\\\\ g_{(x)}=x^4-\sqrt[4]{x^3}\\\\ g_{(x)}=x^4-x^{\frac{3}{4}}}\\\\\\ Derivando\ (aplicando\ a\ regra\ do\ 'tombo'):\\\\ g'_{(x)}=4x^{4-1}-\dfrac{3}{4}x^{\frac{3}{4}-1}}\\\\ g'_{(x)}=4x^3-\dfrac{3}{4}x^{-\frac{1}{4}}}\\\\ g'_{(x)}=4x^3-\dfrac{3}{4}\frac{1}{x^{\frac{1}{4}}}}\\\\ g'_{(x)}=4x^3-\dfrac{3}{4x^{\frac{1}{4}}}}\\\\ g'_{(x)}=4x^3-\dfrac{3}{4\sqrt[4]{x}}}}\\\\ g'_{(x)}=4x^3-\dfrac{3}{4\sqrt[4]{x}}}}\times \dfrac{\sqrt[4]{x}}{\sqrt[4]{x}}$


$\boxed{g'_{(x)}=4x^3-\dfrac{3\sqrt[4]{x}}{4x}}$


Espero ter ajudado.
Bons estudos!