What is the d/(dt)(t/(r-w)) ?

The d/(dt)(t/(r-w)) is (r(t,w)-w-t d/(dt)(r(t,w)))/((r(t,w)-w)^2)

What is the first d/(dt)(t/(r-w)) ?

The first d/(dt)(t/(r-w)) is (r(t,w)-w-t d/(dt)(r(t,w)))/((r(t,w)-w)^2)

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\frac{d}{d t} (\frac{t}{r ( t , w ) - w})

\frac{r ( t , w ) - w - t \frac{d}{d t} ( r ( t , w ) )}{( r ( t , w ) - w ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{t}{r ( t , w ) - w})

Treat

w

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{d t}{d t} ( r ( t , w ) - w ) - \frac{d}{d t} ( r ( t , w ) - w ) t}{( r ( t , w ) - w ) ^{2}}

\frac{d t}{d t} = 1

\frac{d}{d t} (r (t, w) - w) = \frac{d}{d t} (r (t, w))

= \frac{1 \cdot ( r ( t , w ) - w ) - \frac{d}{d t} ( r ( t , w ) ) t}{( r ( t , w ) - w ) ^{2}}

Simplify

= \frac{r ( t , w ) - w - t \frac{d}{d t} ( r ( t , w ) )}{( r ( t , w ) - w ) ^{2}}

2 x + 8 = 440

\frac{3 x - 4}{2} = \frac{9}{4}

4 + 7 (x - 12) = - 38

z = \frac{12 + 9 i}{3 - 4 i}

What is the d/(dt)(t/(r-w)) ?
The d/(dt)(t/(r-w)) is (r(t,w)-w-t d/(dt)(r(t,w)))/((r(t,w)-w)^2)
What is the first d/(dt)(t/(r-w)) ?
The first d/(dt)(t/(r-w)) is (r(t,w)-w-t d/(dt)(r(t,w)))/((r(t,w)-w)^2)