What is the derivative of y= 1/(sqrt(2x-1)) ?

The derivative of y= 1/(sqrt(2x-1)) is -1/((2x-1)^{3/2)}

What is the first derivative of y= 1/(sqrt(2x-1)) ?

The first derivative of y= 1/(sqrt(2x-1)) is -1/((2x-1)^{3/2)}

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = \frac{x ^{3} + 5}{x ^{2} + 1}

\frac{d}{d x} (arccos (2 x^{2}))

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