What is the derivative of x^{-5/4} ?

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

What is the first derivative of x^{-5/4} ?

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

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derivative of

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

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

Solution steps

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{1}{x 9 x ^{2} - 9} d x

\int x^{3} 1 + 36 x^{2} d x

\int (e^{- \frac{x}{5}} + 5 x^{4}) d x

h (t) = (t + 4)^{\frac{2}{3}} (2 t^{2} - 4)^{3}

x \to 7 lim (sec (\frac{π x}{6}))

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