What is the derivative of y=\sqrt[9]{x} ?

The derivative of y=\sqrt[9]{x} is 1/(9x^{8/9)}

What is the first derivative of y=\sqrt[9]{x} ?

The first derivative of y=\sqrt[9]{x} is 1/(9x^{8/9)}

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derivative of

\frac{1}{9 x ^{\frac{8}{9}}}

Solution steps

Apply radical rule:

= \frac{d}{d x} (x^{\frac{1}{9}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{9} x^{\frac{1}{9} - 1}

Simplify

\frac{1}{9} x^{\frac{1}{9} - 1} : \frac{1}{9 x ^{\frac{8}{9}}}

= \frac{1}{9 x ^{\frac{8}{9}}}

\frac{\partial}{\partial z} (5 x^{2} - 3 x y^{2} + x yz)

\int (x^{e} + 10 e^{x}) d x

t sin (5 t)

\int \frac{9 sin ( x )}{cos ^{3} ( x )} d x

x \to 1 lim (x^{\frac{2}{( 1 - x )}})

What is the derivative of y=\sqrt[9]{x} ?
The derivative of y=\sqrt[9]{x} is 1/(9x^{8/9)}
What is the first derivative of y=\sqrt[9]{x} ?
The first derivative of y=\sqrt[9]{x} is 1/(9x^{8/9)}