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

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

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

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

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

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

Solution steps

\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}}

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

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

Simplify

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

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

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