What is (\partial)/(\partial t)((3s+t)/(4s-t)) ?

The answer to (\partial)/(\partial t)((3s+t)/(4s-t)) is (7s)/((4s-t)^2)

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(\partial)/(\partial t)((3s+t)/(4s-t))

\frac{\partial}{\partial t} (\frac{3 s + t}{4 s - t})

\frac{7 s}{( 4 s - t ) ^{2}}

Solution steps

\frac{\partial}{\partial t} (\frac{3 s + t}{4 s - t})

Treat

s

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial t} ( 3 s + t ) ( 4 s - t ) - \frac{\partial}{\partial t} ( 4 s - t ) ( 3 s + t )}{( 4 s - t ) ^{2}}

\frac{\partial}{\partial t} (3 s + t) = 1

\frac{\partial}{\partial t} (4 s - t) = - 1

= \frac{1 \cdot ( 4 s - t ) - ( - 1 ) ( 3 s + t )}{( 4 s - t ) ^{2}}

Simplify

\frac{1 \cdot ( 4 s - t ) - ( - 1 ) ( 3 s + t )}{( 4 s - t ) ^{2}} : \frac{7 s}{( 4 s - t ) ^{2}}

= \frac{7 s}{( 4 s - t ) ^{2}}

What is (\partial)/(\partial t)((3s+t)/(4s-t)) ?
The answer to (\partial)/(\partial t)((3s+t)/(4s-t)) is (7s)/((4s-t)^2)