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

The derivative of 1/(1+2x) is -2/((1+2x)^2)

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

The first derivative of 1/(1+2x) is -2/((1+2x)^2)

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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