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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1}{4 - 9 x ^{2}} d x

x \to 3 lim (6 - 2 x)

\int 3 x ln (2 x) d x

y = x (6 x + 1)^{5}

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