Question

Derivada de
$y=x^3 \sqrt[4]{x^3}$

Answer 1

$\\ y = x^3 \sqrt[4]{x^3} \\ \\ y = x^3*x^3^/^4 \\ \\ y = x^3^+^3^/^4 \\ \\ y = x^1^2^/^4^+^3^/^4 \\ \\ y = x^1^5^/^4$

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$\\ y' = \frac{15}{4} *x^1^5^/^4-^1 \\ \\ y' = \frac{15}{4} *x^1^5^/^4^-^4^/^4 \\ \\ y' = \frac{15}{4} *x^1^1^/^4 \\ \\ y' = \frac{15x^1^1^/^4}{4} \\ \\ y' = \frac{15 \sqrt[4]{x^1^1} }{4}$

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Answer 2

$\sf \displaystyle \large{y=x^3\sqrt[\sf 4]{\sf x^3}}\\\\\\\large{\frac{d}{dx}\left(x^3\sqrt[\sf 4]{\sf x^3}\right)}\\\\\\\large{=\frac{d}{dx}\left(x^3\right)\sqrt[\sf 4]{\sf x^3}+\frac{d}{dx}\left(\sqrt[\sf 4]{\sf x^3}\right)x^3}\\\\\\\large{=3x^2\sqrt[\sf 4]{\sf x^3}+\frac{3x^2}{4\left(x^3\right)^{\frac{3}{4}}}x^3}\\\\\\\to \boxed{\sf\large{ =3x^2\sqrt[\sf 4]{\sf x^3}+\frac{3x^5}{4\left(x^3\right)^{\frac{3}{4}}}}}$