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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d 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}}

(1 + cos (t)) y^{^{'}} = (1 + e^{- y}) sin (t)

\frac{d}{d x} (lo g_{4} (2 x + 3))

f (x) = (5 t^{2} - 2 t + 1)^{\frac{3}{2}}

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

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