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Popular >

derivative of 1/(2x+2)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

slope of (-3.3)(5.9)slope

(- 3.3) (5.9)

(\partial)/(\partial y)(e^{2y})

\frac{\partial}{\partial y} (e^{2 y})

integral of (2x)/(x^2+5)

\int \frac{2 x}{x ^{2} + 5} d x

integral from 0 to 2 of (2x)/((x^2+5)^2)

\int_{0}^{2} \frac{2 x}{( x ^{2} + 5 ) ^{2}} d x

derivative of (ln(x)^{1/2})

\frac{d}{d x} ((ln (x))^{\frac{1}{2}})

Frequently Asked Questions (FAQ)

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