What is (\partial)/(\partial x)(a/(x^2+a^2)) ?

The answer to (\partial)/(\partial x)(a/(x^2+a^2)) is -(2ax)/((x^2+a^2)^2)

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(\partial)/(\partial x)(a/(x^2+a^2))

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

ln (8 x + 9)

\int (a^{\frac{2}{3}} - x^{\frac{2}{3}}) d x

\int \frac{1}{36 - 4 x ^{2}} d x

\int (4 - 2 x) d x

\frac{d}{d x} (sin (x) + x)

What is (\partial)/(\partial x)(a/(x^2+a^2)) ?
The answer to (\partial)/(\partial x)(a/(x^2+a^2)) is -(2ax)/((x^2+a^2)^2)