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})

\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})

\frac{s - 1}{s ^{2} + 4 s + 5}

\frac{\partial}{\partial x} (e^{- 5 x} cos (7 π t))

\int sin (2 x) - cos (x) d x

\int_{0}^{2} x^{4} d x

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}