What is the derivative of 4x^{(-1/8}) ?

The derivative of 4x^{(-1/8}) is -1/(2x^{9/8)}

What is the first derivative of 4x^{(-1/8}) ?

The first derivative of 4x^{(-1/8}) is -1/(2x^{9/8)}

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\frac{d}{d x} (4 x^{\frac{- 1}{8}})

- \frac{1}{2 x ^{\frac{9}{8}}}

Solution steps

\frac{d}{d x} (4 x^{\frac{- 1}{8}})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{\frac{- 1}{8}})

Apply the Power Rule:

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

= 4 \cdot \frac{- 1}{8} x^{\frac{- 1}{8} - 1}

Simplify

4 \cdot \frac{- 1}{8} x^{\frac{- 1}{8} - 1} : - \frac{1}{2 x ^{\frac{9}{8}}}

= - \frac{1}{2 x ^{\frac{9}{8}}}

What is the derivative of 4x^{(-1/8}) ?
The derivative of 4x^{(-1/8}) is -1/(2x^{9/8)}
What is the first derivative of 4x^{(-1/8}) ?
The first derivative of 4x^{(-1/8}) is -1/(2x^{9/8)}