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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

x \to 0 + lim (x ln (x^{5}))

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

x^{2} + y^{2} = 27, at x = 3

\int x sin (x^{2} + 4) d x

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