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

The derivative of 1/(2x^{1/2}) is -1/(4x^{3/2)}

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

The first derivative of 1/(2x^{1/2}) is -1/(4x^{3/2)}

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

- \frac{1}{4 x ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Simplify

\frac{1}{2} (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{1}{4 x ^{\frac{3}{2}}}

= - \frac{1}{4 x ^{\frac{3}{2}}}

What is the derivative of 1/(2x^{1/2}) ?
The derivative of 1/(2x^{1/2}) is -1/(4x^{3/2)}
What is the first derivative of 1/(2x^{1/2}) ?
The first derivative of 1/(2x^{1/2}) is -1/(4x^{3/2)}