derivada de
![y=6 \sqrt[3]{x^2}- \frac{4}{ \sqrt{x} }](https://tex.z-dn.net/?f=y%3D6++%5Csqrt%5B3%5D%7Bx%5E2%7D-++%5Cfrac%7B4%7D%7B+%5Csqrt%7Bx%7D+%7D+ "y=6 \sqrt[3]{x^2}- \frac{4}{ \sqrt{x} }")
Soluções para a tarefa
Respondido por
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Vamos tirar da raiz:
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![\\ y' = 6* \frac{2}{3} *x^2^/^3^-^1-4* \frac{-1}{2} *x^-^1^/^2^-^1
\\
\\y' = 4x^2^/^3^-^3^/^3 +2x^-^1^/^2^-^2^/^2
\\
\\ y' = 4x^-^1^/^3 +2x^-^3^/^2
\\
\\ y' = \frac{4}{x^1^/^3 } + \frac{2}{x^3^/^2}
\\
\\ y' = \frac{4*x^3^/^2+2*x^1^/^3}{x^1^/^3 *x^3^/^2}
\\
\\ y' = \frac{4 \sqrt[2]{x^3} +2 \sqrt[3]{x} }{x^1^/^3^+^3^/^2}
\\
\\ y' = \frac{4 \sqrt[2]{x^3} +2 \sqrt[3]{x}}{x^1^1^/^9}
\\
\\ y' = \frac{4 \sqrt[2]{x^3} +2 \sqrt[3]{x}}{ \sqrt[9]{x^1^1} }](https://tex.z-dn.net/?f=+%5C%5C+y%27+%3D+6%2A+%5Cfrac%7B2%7D%7B3%7D+%2Ax%5E2%5E%2F%5E3%5E-%5E1-4%2A+%5Cfrac%7B-1%7D%7B2%7D+%2Ax%5E-%5E1%5E%2F%5E2%5E-%5E1%0A+%5C%5C+%0A+%5C%5Cy%27+%3D+4x%5E2%5E%2F%5E3%5E-%5E3%5E%2F%5E3+%2B2x%5E-%5E1%5E%2F%5E2%5E-%5E2%5E%2F%5E2%0A+%5C%5C+%0A+%5C%5C+y%27+%3D+4x%5E-%5E1%5E%2F%5E3+%2B2x%5E-%5E3%5E%2F%5E2%0A+%5C%5C+%0A+%5C%5C+y%27+%3D++%5Cfrac%7B4%7D%7Bx%5E1%5E%2F%5E3+%7D+%2B++%5Cfrac%7B2%7D%7Bx%5E3%5E%2F%5E2%7D+%0A+%5C%5C+%0A+%5C%5C+y%27+%3D++%5Cfrac%7B4%2Ax%5E3%5E%2F%5E2%2B2%2Ax%5E1%5E%2F%5E3%7D%7Bx%5E1%5E%2F%5E3+%2Ax%5E3%5E%2F%5E2%7D+%0A+%5C%5C+%0A+%5C%5C+y%27+%3D++%5Cfrac%7B4+%5Csqrt%5B2%5D%7Bx%5E3%7D+%2B2+%5Csqrt%5B3%5D%7Bx%7D+%7D%7Bx%5E1%5E%2F%5E3%5E%2B%5E3%5E%2F%5E2%7D+%0A+%5C%5C+%0A+%5C%5C+y%27+%3D++%5Cfrac%7B4+%5Csqrt%5B2%5D%7Bx%5E3%7D+%2B2+%5Csqrt%5B3%5D%7Bx%7D%7D%7Bx%5E1%5E1%5E%2F%5E9%7D+%0A+%5C%5C+%0A+%5C%5C+y%27+%3D++%5Cfrac%7B4+%5Csqrt%5B2%5D%7Bx%5E3%7D+%2B2+%5Csqrt%5B3%5D%7Bx%7D%7D%7B+%5Csqrt%5B9%5D%7Bx%5E1%5E1%7D+%7D+ "\\ y' = 6* \frac{2}{3} *x^2^/^3^-^1-4* \frac{-1}{2} *x^-^1^/^2^-^1
\\
\\y' = 4x^2^/^3^-^3^/^3 +2x^-^1^/^2^-^2^/^2
\\
\\ y' = 4x^-^1^/^3 +2x^-^3^/^2
\\
\\ y' = \frac{4}{x^1^/^3 } + \frac{2}{x^3^/^2}
\\
\\ y' = \frac{4*x^3^/^2+2*x^1^/^3}{x^1^/^3 *x^3^/^2}
\\
\\ y' = \frac{4 \sqrt[2]{x^3} +2 \sqrt[3]{x} }{x^1^/^3^+^3^/^2}
\\
\\ y' = \frac{4 \sqrt[2]{x^3} +2 \sqrt[3]{x}}{x^1^1^/^9}
\\
\\ y' = \frac{4 \sqrt[2]{x^3} +2 \sqrt[3]{x}}{ \sqrt[9]{x^1^1} }")
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