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

The answer to (\partial)/(\partial x)((4x-3t)/(s+2x)) is (4s+6t)/((s+2x)^2)

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

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

\frac{4 s + 6 t}{( s + 2 x ) ^{2}}

Solution steps

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

Treat

t, s

as constants

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

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

\frac{\partial}{\partial x} (s + 2 x) = 2

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

Expand

4 (s + 2 x) - 2 (4 x - 3 t) : 4 s + 6 t

= \frac{4 s + 6 t}{( s + 2 x ) ^{2}}

\frac{\partial}{\partial x} (x - cos (x))

y^{^{'}} = y x

x \to 0 lim (+ \frac{x ^{3} + 3}{x})

\frac{d}{d x} (ln (3 - x^{2}))

\frac{d}{d x} (24 + x^{2})

What is (\partial)/(\partial x)((4x-3t)/(s+2x)) ?
The answer to (\partial)/(\partial x)((4x-3t)/(s+2x)) is (4s+6t)/((s+2x)^2)