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

The derivative of 4/(x^2+1) is -(8x)/((x^2+1)^2)

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

The first derivative of 4/(x^2+1) is -(8x)/((x^2+1)^2)

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

- \frac{8 x}{( x ^{2} + 1 ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= 4 \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

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

Simplify

4 (- \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 2 x) : - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

x \to 0 lim (\frac{1}{2 x} - \frac{1}{e ^{2 x} - 1})

\frac{\partial}{\partial x} (x^{2})

7 x - 2 x

y = 20 x^{3} (x^{4} + 5)^{4}

\int_{0}^{4} (x - 4)^{2} d x

What is the derivative of 4/(x^2+1) ?
The derivative of 4/(x^2+1) is -(8x)/((x^2+1)^2)
What is the first derivative of 4/(x^2+1) ?
The first derivative of 4/(x^2+1) is -(8x)/((x^2+1)^2)