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

The answer to (\partial)/(\partial x)((4x-3y)/(4x+3y)) is (24y)/((4x+3y)^2)

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(\partial)/(\partial x)((4x-3y)/(4x+3y))

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

\frac{24 y}{( 4 x + 3 y ) ^{2}}

Solution steps

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

Treat

y

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

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

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

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

Expand

4 (4 x + 3 y) - 4 (4 x - 3 y) : 24 y

= \frac{24 y}{( 4 x + 3 y ) ^{2}}

f (x) = - 16 t^{2} - 8 t + 64

(x^{2} - 3) (x^{3} - 2 x)

\int_{0}^{\frac{π}{4}} (cos (2 x)) d x

y^{^{''}} + 2 y^{^{'}} + 5 y = - 2 t + 4 t^{2}

\frac{d}{d x} (\frac{3}{x ^{3}} - \frac{1}{x ^{4}})

What is (\partial)/(\partial x)((4x-3y)/(4x+3y)) ?
The answer to (\partial)/(\partial x)((4x-3y)/(4x+3y)) is (24y)/((4x+3y)^2)