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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Graph

Popular Examples

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\int_{0}^{6} x^{2} 36 - x^{2} d x

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y = \frac{3 x ^{5} - 7 x ^{2} - 4}{x ^{2}}

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Frequently Asked Questions (FAQ)

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