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

The derivative of 2x^{(-1)/2} is -1/(x^{3/2)}

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

The first derivative of 2x^{(-1)/2} is -1/(x^{3/2)}

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derivative of

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

- \frac{1}{x ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

= 2 \cdot \frac{- 1}{2} x^{\frac{- 1}{2} - 1}

Simplify

2 \cdot \frac{- 1}{2} x^{\frac{- 1}{2} - 1} : - \frac{1}{x ^{\frac{3}{2}}}

= - \frac{1}{x ^{\frac{3}{2}}}

1 + 6 x

9 e^{- 3} x^{2}

\frac{x + 1 - 4}{( - x + 3 )}

1 + 7 x

5 x^{2} + 9 x + c

What is the derivative of 2x^{(-1)/2} ?
The derivative of 2x^{(-1)/2} is -1/(x^{3/2)}
What is the first derivative of 2x^{(-1)/2} ?
The first derivative of 2x^{(-1)/2} is -1/(x^{3/2)}