What is (\partial)/(\partial x)(1/(2x+1)) ?

The answer to (\partial)/(\partial x)(1/(2x+1)) is -2/((2x+1)^2)

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(\partial)/(\partial x)(1/(2x+1))

\frac{\partial}{\partial x} (\frac{1}{2 x + 1})

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

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2 x + 1})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (2 x + 1) = 2

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

Simplify

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

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

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What is (\partial)/(\partial x)(1/(2x+1)) ?
The answer to (\partial)/(\partial x)(1/(2x+1)) is -2/((2x+1)^2)