What is the derivative of v/x ?

The derivative of v/x is (x\frac{dv)/(dx)-v}{x^2}

What is the first derivative of v/x ?

The first derivative of v/x is (x\frac{dv)/(dx)-v}{x^2}

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\frac{d}{d x} (\frac{v ( x )}{x})

\frac{x \frac{d v}{d x} - v}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{v}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d v}{d x} x - \frac{d x}{d x} v}{x ^{2}}

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

= \frac{\frac{d v}{d x} x - 1 \cdot v}{x ^{2}}

Simplify

= \frac{x \frac{d v}{d x} - v}{x ^{2}}

\frac{d}{d x} (\frac{x ^{3}}{x - 1})

in v erse l a pl a ce \frac{s - 1}{s ^{2} + 4 s + 5}

\frac{\partial}{\partial x} (e^{x} cos (x))

d er i v a t i v e f (x) = x^{2} + 5

\frac{d}{d x} (cos (2 x + π))

What is the derivative of v/x ?
The derivative of v/x is (x\frac{dv)/(dx)-v}{x^2}
What is the first derivative of v/x ?
The first derivative of v/x is (x\frac{dv)/(dx)-v}{x^2}