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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x^{2} y - x y^{3})

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

\int 100 q^{- 0.5} d q

\int \frac{x ^{5}}{x ^{6} + 3} d x

24 x

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