What is (\partial)/(\partial x)((4x+3t)/(x-2t)) ?

The answer to (\partial)/(\partial x)((4x+3t)/(x-2t)) is -(11t)/((x-2t)^2)

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(\partial)/(\partial x)((4x+3t)/(x-2t))

\frac{\partial}{\partial x} (\frac{4 x + 3 t}{x - 2 t})

- \frac{11 t}{( x - 2 t ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{4 x + 3 t}{x - 2 t})

Treat

t

as a constant

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (4 x + 3 t) = 4

\frac{\partial}{\partial x} (x - 2 t) = 1

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

Simplify

\frac{4 ( x - 2 t ) - 1 \cdot ( 4 x + 3 t )}{( x - 2 t ) ^{2}} : - \frac{11 t}{( x - 2 t ) ^{2}}

= - \frac{11 t}{( x - 2 t ) ^{2}}

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What is (\partial)/(\partial x)((4x+3t)/(x-2t)) ?
The answer to (\partial)/(\partial x)((4x+3t)/(x-2t)) is -(11t)/((x-2t)^2)