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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\int (x^{4} + 2 x - 16) d x

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

\frac{d}{d x} (a (1 - cos (x)))

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

\int_{1}^{5} \frac{1}{( x - 4 ) ^{2}} d x

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