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)}

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derivative of

\frac{1}{2 x}

- \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}}}

3 ln (e^{x})

y = sin^{3} (1 - 2 x)

(x^{2} + 1)^{\frac{1}{2}} - 1

\frac{1}{sin ( x - y )}

(x + 1) (x - 2)^{2}

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)}