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Popular Calculus >

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}}}

Graph

Popular Examples

inverse oflaplace 1/((s(s^2+6s-27)))

in v erse l a pl a ce \frac{1}{( s ( s ^{2} + 6 s - 27 ) )}

(dy}{dx}=\frac{y+1)/x

\frac{d y}{d x} = \frac{y + 1}{x}

derivative of (3x-1)/((x-1)^3)

d er i v a t i v e \frac{3 x - 1}{( x - 1 ) ^{3}}

integral of 6x+2

\int 6 x + 2 d x

derivative of (x+2)^3-e^{3x}

d er i v a t i v e (x + 2)^{3} - e^{3 x}

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)}