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

The derivative of 1/((2x+1)^2) is -4/((2x+1)^3)

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

The first derivative of 1/((2x+1)^2) is -4/((2x+1)^3)

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derivative of

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

- \frac{4}{( 2 x + 1 ) ^{3}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= - \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2

Simplify

- \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2 : - \frac{4}{( 2 x + 1 ) ^{3}}

= - \frac{4}{( 2 x + 1 ) ^{3}}

\int \frac{1}{x ^{2} 4 x ^{2} - 25} d x

t^{2} (5 t + 2)^{3}

\int e^{4 x - 7} d x

f (x) = cot^{2} (x)

\int e^{0.04 x} d x

What is the derivative of 1/((2x+1)^2) ?
The derivative of 1/((2x+1)^2) is -4/((2x+1)^3)
What is the first derivative of 1/((2x+1)^2) ?
The first derivative of 1/((2x+1)^2) is -4/((2x+1)^3)