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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

e^{3 x} \cdot sin (ln (x))

4 t^{2} + 3 t + 3

y = x^{2} - 4 x + 1

lo g_{10} (2 - x)

\frac{d}{d x} (a \cdot e^{2 x} + b \cdot e^{- 3 x} + c \cdot e^{x})

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