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

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

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

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

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derivative of

\frac{1}{4 + x ^{2}}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{\frac{π}{2}} (sin^{3} (x)) d x

n = 2 \sum \infty \frac{n}{3 ^{n + 1}}

ln (\frac{8 - x}{8 + x})

72 x - \frac{4 x ^{3}}{3}

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

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