What is the derivative of f(x)=2x^{-1/4} ?

The derivative of f(x)=2x^{-1/4} is -1/(2x^{5/4)}

What is the first derivative of f(x)=2x^{-1/4} ?

The first derivative of f(x)=2x^{-1/4} is -1/(2x^{5/4)}

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derivative of

f (x) = 2 x^{- \frac{1}{4}}

- \frac{1}{2 x ^{\frac{5}{4}}}

Solution steps

\frac{d}{d x} (2 x^{- \frac{1}{4}})

Take the constant out:

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

= 2 \frac{d}{d x} (x^{- \frac{1}{4}})

Apply the Power Rule:

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

= 2 (- \frac{1}{4} x^{- \frac{1}{4} - 1})

Simplify

2 (- \frac{1}{4} x^{- \frac{1}{4} - 1}) : - \frac{1}{2 x ^{\frac{5}{4}}}

= - \frac{1}{2 x ^{\frac{5}{4}}}

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What is the derivative of f(x)=2x^{-1/4} ?
The derivative of f(x)=2x^{-1/4} is -1/(2x^{5/4)}
What is the first derivative of f(x)=2x^{-1/4} ?
The first derivative of f(x)=2x^{-1/4} is -1/(2x^{5/4)}