What is the derivative of 1/(5x^{4/5)} ?

The derivative of 1/(5x^{4/5)} is -4/(25x^{9/5)}

What is the first derivative of 1/(5x^{4/5)} ?

The first derivative of 1/(5x^{4/5)} is -4/(25x^{9/5)}

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derivative of

\frac{1}{5 x ^{\frac{4}{5}}}

- \frac{4}{25 x ^{\frac{9}{5}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{5} (- \frac{4}{5} x^{- \frac{4}{5} - 1}) : - \frac{4}{25 x ^{\frac{9}{5}}}

= - \frac{4}{25 x ^{\frac{9}{5}}}

f (x) = \frac{x ^{3} + 1}{x ^{3} - 1}

x^{3} y^{^{'''}} + x y^{^{'}} - y = 0

\int e^{- 1}

f (x) = \frac{2 ln ( x )}{x}

\frac{\partial}{\partial x} (2 x (4 + y)^{- 1})

What is the derivative of 1/(5x^{4/5)} ?
The derivative of 1/(5x^{4/5)} is -4/(25x^{9/5)}
What is the first derivative of 1/(5x^{4/5)} ?
The first derivative of 1/(5x^{4/5)} is -4/(25x^{9/5)}