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

The derivative of-1/(2x^{3/2}) is 3/(4x^{5/2)}

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

The first derivative of-1/(2x^{3/2}) is 3/(4x^{5/2)}

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

\frac{3}{4 x ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

= - \frac{1}{2} \frac{d}{d x} (\frac{1}{x ^{\frac{3}{2}}})

Apply exponent rule:

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

= - \frac{1}{2} \frac{d}{d x} (x^{- \frac{3}{2}})

Apply the Power Rule:

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

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

Simplify

- \frac{1}{2} (- \frac{3}{2} x^{- \frac{3}{2} - 1}) : \frac{3}{4 x ^{\frac{5}{2}}}

= \frac{3}{4 x ^{\frac{5}{2}}}

What is the derivative of-1/(2x^{3/2}) ?
The derivative of-1/(2x^{3/2}) is 3/(4x^{5/2)}
What is the first derivative of-1/(2x^{3/2}) ?
The first derivative of-1/(2x^{3/2}) is 3/(4x^{5/2)}