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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Power Rule:

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

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

Simplify

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

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

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

(e^{x} + e^{- x})^{2}

3^{x} - e^{x} + 5^{x} \cdot ln (x) + 3^{3}

(x + 7)^{5}

y = \frac{( x ^{2} + 2 x + 1 )}{( x + 1 )}

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