What is the derivative of x^{-1/4} ?

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

What is the first derivative of x^{-1/4} ?

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

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

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

Solution steps

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

Apply the Power Rule:

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

= - \frac{1}{4} x^{- \frac{1}{4} - 1}

Simplify

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

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

\frac{d}{d x} (\frac{250}{1 + 4 e ^{- 0.75 x}})

\int \frac{- e ^{4 x}}{4 x} d x

\int 27 x^{2} cos (3 x) d x

(5, - 5), (1, 5)

\int - \frac{1000}{x ^{2}} d x

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