What is (\partial)/(\partial v)(v/(u-v)) ?

The answer to (\partial)/(\partial v)(v/(u-v)) is u/((u-v)^2)

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(\partial)/(\partial v)(v/(u-v))

\frac{\partial}{\partial v} (\frac{v}{u - v})

\frac{u}{( u - v ) ^{2}}

Solution steps

\frac{\partial}{\partial v} (\frac{v}{u - v})

Treat

u

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial v} ( v ) ( u - v ) - \frac{\partial}{\partial v} ( u - v ) v}{( u - v ) ^{2}}

\frac{\partial}{\partial v} (v) = 1

\frac{\partial}{\partial v} (u - v) = - 1

= \frac{1 \cdot ( u - v ) - ( - 1 ) v}{( u - v ) ^{2}}

Simplify

\frac{1 \cdot ( u - v ) - ( - 1 ) v}{( u - v ) ^{2}} : \frac{u}{( u - v ) ^{2}}

= \frac{u}{( u - v ) ^{2}}

\frac{d}{d x} (\frac{x ^{3}}{5})

y = x^{2} - 5, (- 3, 4)

(1, 2), (- 2, - 1)

\int \frac{3 x}{1 - x ^{4}} d x

\int 36 e^{6 x} sin (6 x) d x

What is (\partial)/(\partial v)(v/(u-v)) ?
The answer to (\partial)/(\partial v)(v/(u-v)) is u/((u-v)^2)