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

The derivative of a/((x^2+a^2^2)) is -(4ax)/((x^2+a^2)^3)

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

The first derivative of a/((x^2+a^2^2)) is -(4ax)/((x^2+a^2)^3)

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

- \frac{4 a x}{( x ^{2} + a ^{2} ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= a (- \frac{2}{( x ^{2} + a ^{2} ) ^{3}} \cdot 2 x)

Simplify

a (- \frac{2}{( x ^{2} + a ^{2} ) ^{3}} \cdot 2 x) : - \frac{4 a x}{( x ^{2} + a ^{2} ) ^{3}}

= - \frac{4 a x}{( x ^{2} + a ^{2} ) ^{3}}

\frac{d}{d x} (x^{3} + 3 x^{2} + 3 x + 1)

\frac{\partial}{\partial x} (3^{2 x} + 5^{4 y} + 2 x + y^{4})

\frac{d}{d x} ((x^{3} + x^{2}) e^{2 x})

\int x 2 - \frac{1}{2 x} d x

x \to 0 lim (\frac{x + 6}{x ^{2} + 3})

What is the derivative of a/((x^2+a^2^2)) ?
The derivative of a/((x^2+a^2^2)) is -(4ax)/((x^2+a^2)^3)
What is the first derivative of a/((x^2+a^2^2)) ?
The first derivative of a/((x^2+a^2^2)) is -(4ax)/((x^2+a^2)^3)