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

The derivative of a/(x^2+b) is -(2ax)/((x^2+b)^2)

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

The first derivative of a/(x^2+b) is -(2ax)/((x^2+b)^2)

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\frac{d}{d x} (\frac{a}{x ^{2} + b})

- \frac{2 a x}{( x ^{2} + b ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{a}{x ^{2} + b})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = x^{8}

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

\int x cos (\frac{nπ x}{l}) d x

\int (4 x + 2) ln (x + 1) d x

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

What is the derivative of a/(x^2+b) ?
The derivative of a/(x^2+b) is -(2ax)/((x^2+b)^2)
What is the first derivative of a/(x^2+b) ?
The first derivative of a/(x^2+b) is -(2ax)/((x^2+b)^2)