What is the derivative of 1/(sqrt(2x+1)) ?

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

What is the first derivative of 1/(sqrt(2x+1)) ?

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

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\frac{d}{d x} (\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}}}

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