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Popular >

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

Solution

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

Solution

- \frac{3}{8 x ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{1}{x ^{\frac{3}{2}}})

Apply exponent rule:

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

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

Simplify

\frac{1}{4} (- \frac{3}{2} x^{- \frac{3}{2} - 1}) : - \frac{3}{8 x ^{\frac{5}{2}}}

= - \frac{3}{8 x ^{\frac{5}{2}}}

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y^{^{''}} - 9 y^{^{'}} + 18 y = - 4 cos (3 t)

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Frequently Asked Questions (FAQ)

What is the derivative of 1/(4x^{3/2}) ?
The derivative of 1/(4x^{3/2}) is -3/(8x^{5/2)}
What is the first derivative of 1/(4x^{3/2}) ?
The first derivative of 1/(4x^{3/2}) is -3/(8x^{5/2)}