What is (\partial)/(\partial x)((5x-3y)/(5x+3y)) ?

The answer to (\partial)/(\partial x)((5x-3y)/(5x+3y)) is (30y)/((5x+3y)^2)

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(\partial)/(\partial x)((5x-3y)/(5x+3y))

\frac{\partial}{\partial x} (\frac{5 x - 3 y}{5 x + 3 y})

\frac{30 y}{( 5 x + 3 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{5 x - 3 y}{5 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} ( 5 x - 3 y ) ( 5 x + 3 y ) - \frac{\partial}{\partial x} ( 5 x + 3 y ) ( 5 x - 3 y )}{( 5 x + 3 y ) ^{2}}

\frac{\partial}{\partial x} (5 x - 3 y) = 5

\frac{\partial}{\partial x} (5 x + 3 y) = 5

= \frac{5 ( 5 x + 3 y ) - 5 ( 5 x - 3 y )}{( 5 x + 3 y ) ^{2}}

Expand

5 (5 x + 3 y) - 5 (5 x - 3 y) : 30 y

= \frac{30 y}{( 5 x + 3 y ) ^{2}}

\int x^{2} cos (x^{3}) d x

x \to 1 lim (- x^{2} + 9 x - 7)

(1 + e^{x}) \frac{d y}{d x} + e^{x} y = 0

\int \frac{3 x}{x + 2} d x

y^{^{'}} = 0.05 y + 5500

What is (\partial)/(\partial x)((5x-3y)/(5x+3y)) ?
The answer to (\partial)/(\partial x)((5x-3y)/(5x+3y)) is (30y)/((5x+3y)^2)