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Popular >

derivative of 1/2 x^{3/2}

Solution

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

Solution

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

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} (x^{\frac{3}{2}})

Apply the Power Rule:

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

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

Simplify

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

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

Popular Examples

integral of (3t+2)/(t+1)

\int \frac{3 t + 2}{t + 1} d t

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\frac{d}{d x} (e)

derivative of (12800)/(1+10e^{-0.5x)}derivative of

\frac{12800}{1 + 10 e ^{- 0.5 x}}

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\frac{d}{d x} (7 - \frac{1}{3} x)

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\int_{0}^{1} (x^{2} + 5) (e^{- x}) d x

Frequently Asked Questions (FAQ)

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