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Popular >

derivative of 1/(sqrt(2x))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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\frac{3 v + v ^{2}}{v + 1} = x \frac{d v}{d x} + v

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Frequently Asked Questions (FAQ)

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