How do you find the derivative of $\sqrt[6]{x^{5}}$ $root6(x^5)$ ?

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How do you find the derivative of $\sqrt[6]{x^{5}}$ $root6(x^5)$ ?

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Answer 1 · 2018-04-12T05:14:34

$= \frac{5}{6 \sqrt[6]{x}}$ $=5/(6root(6)x)$

Explanation:

$f (x) = \sqrt[6]{x^{5}} = x^{\frac{5}{6}}$ $f(x)=root(6)(x^5)=x^(5/6)$
$\frac{d}{d x} f (x) = \frac{5}{6} x^{\frac{5}{6} - 1}$ $d/dx f(x)=5/6x^(5/6-1)$
$= \frac{5}{6} x^{- \frac{1}{6}}$ $=5/6x^(-1/6)$
$= \frac{5}{6 \sqrt[6]{x}}$ $=5/(6root(6)x)$

Answer 2 · 2018-04-12T05:16:11

Derivative of ${\sqrt[6]{x}}^{5}$ $root(6)x^5$ is $\frac{5}{6 \sqrt[6]{x}}$ $5/(6root(6)x)$

Explanation:

The derivative of $x^{n}$ $x^n$ is $n x^{n - 1}$ $nx^(n-1)$

As we can write ${\sqrt[6]{x}}^{5} = x^{\frac{5}{6}}$ $root(6)x^5=x^(5/6)$

$\frac{d}{d x} {\sqrt[6]{x}}^{5} = \frac{5}{6} x^{\frac{5}{6} - 1}$ $d/(dx)root(6)x^5=5/6x^(5/6-1)$

= $\frac{5}{6} x^{- \frac{1}{6}}$ $5/6x^(-1/6)$

= $\frac{5}{6} \cdot \frac{1}{\sqrt[6]{x}}$ $5/6*1/root(6)x$

= $\frac{5}{6 \sqrt[6]{x}}$ $5/(6root(6)x)$

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How do you find the derivative of $\sqrt[6]{x^{5}}$ $root6(x^5)$ ?

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