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{d}{d x} (5 x^{8})

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

Solution steps

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

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

y^{^{'}} = 2 y

\frac{d}{d x} (\frac{x ^{9} e ^{x}}{x ^{9} + e ^{x}})

ma c l a u r in cos (θ)

im pl i c i t \frac{d y}{d x}, (3 x y + 7)^{2} = 6 y

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