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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\frac{d}{d x} (\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}}}

\int w d w

\int x^{3} + 2 x d x

\frac{d y}{d x} = 1 - x - y

f (x) = - 8 x^{2} + 5 x, at x = - 1

\int 5 x + c d x

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)}