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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(x^{2} + 2 x) (1 - e^{x})

\frac{d}{d x} (\frac{x + 4}{x ^{3} + x - 5})

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

8 x + x

\int \frac{x ^{6} - x}{x ^{3}} d x

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