What is the d/(dv)(v/(u-v)) ?

The d/(dv)(v/(u-v)) is u/((u-v)^2)

What is the first d/(dv)(v/(u-v)) ?

The first d/(dv)(v/(u-v)) is u/((u-v)^2)

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

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

Solution steps

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

\frac{d v}{d v} = 1

\frac{d}{d 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}}

16 y^{^{''}} - y = 0

\frac{d}{d x} (5 x 2)

\frac{\partial}{\partial x} (x sin (v))

\frac{d}{d x} (cosh^{2} (x) - sinh^{2} (x))