What is the derivative of (2x+1^{-1}) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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}}

\int \frac{arcsin ( x )}{x} d x

y^{^{''}} + 16 y^{^{'}} + 80 y = 0

\frac{d}{d x} (- x^{3} + 3 x^{2} + 9 x - 1)

e^{2 x}, - 2

\int \frac{1}{- x ^{2} + 249 x + 250} d x

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