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Popular >

derivative of 1/((1+2x))

Solution

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

Solution

- \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}}

Popular Examples

derivative of (-16x^2+36^2)

\frac{d}{d x} ((- 16 x^{2} + 36)^{2})

derivative of x/(1-ln(x-3))

\frac{d}{d x} (\frac{x}{1 - ln ( x - 3 )})

limit as x approaches 0 of (4^x-2^x)/x

x \to 0 lim (\frac{4 ^{x} - 2 ^{x}}{x})

derivative of a-bx^2

\frac{d}{d x} (a - b x^{2})

integral from 1 to 2 of (2x-3)^2

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

Frequently Asked Questions (FAQ)

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)