What is the derivative of \sqrt[5]{x^8} ?

The derivative of \sqrt[5]{x^8} is (8x^{3/5})/5

What is the first derivative of \sqrt[5]{x^8} ?

The first derivative of \sqrt[5]{x^8} is (8x^{3/5})/5

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\frac{8 x ^{\frac{3}{5}}}{5}

Solution steps

Apply the chain rule:

\frac{1}{5 ( x ^{8} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{8})

= \frac{1}{5 ( x ^{8} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{1}{5 ( x ^{8} ) ^{\frac{4}{5}}} \cdot 8 x^{7}

Simplify

\frac{1}{5 ( x ^{8} ) ^{\frac{4}{5}}} \cdot 8 x^{7} : \frac{8 x ^{\frac{3}{5}}}{5}

= \frac{8 x ^{\frac{3}{5}}}{5}

\frac{\partial}{\partial x} (ln (x + 4 y + 2 z))

\int_{- 2}^{3} (x^{2} - 3) d x

\frac{d}{d x} (sin (x + 2 y))

y^{^{'}} = 2 y

\frac{d}{d x} (\frac{1}{x ^{2} + 2})

What is the derivative of \sqrt[5]{x^8} ?
The derivative of \sqrt[5]{x^8} is (8x^{3/5})/5
What is the first derivative of \sqrt[5]{x^8} ?
The first derivative of \sqrt[5]{x^8} is (8x^{3/5})/5