What is (\partial)/(\partial x)((6x-9y)/(6x+9y)) ?

The answer to (\partial)/(\partial x)((6x-9y)/(6x+9y)) is (12y)/((2x+3y)^2)

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(\partial)/(\partial x)((6x-9y)/(6x+9y))

\frac{\partial}{\partial x} (\frac{6 x - 9 y}{6 x + 9 y})

\frac{12 y}{( 2 x + 3 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{6 x - 9 y}{6 x + 9 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} ( 6 x - 9 y ) ( 6 x + 9 y ) - \frac{\partial}{\partial x} ( 6 x + 9 y ) ( 6 x - 9 y )}{( 6 x + 9 y ) ^{2}}

\frac{\partial}{\partial x} (6 x - 9 y) = 6

\frac{\partial}{\partial x} (6 x + 9 y) = 6

= \frac{6 ( 6 x + 9 y ) - 6 ( 6 x - 9 y )}{( 6 x + 9 y ) ^{2}}

Simplify

\frac{6 ( 6 x + 9 y ) - 6 ( 6 x - 9 y )}{( 6 x + 9 y ) ^{2}} : \frac{12 y}{( 2 x + 3 y ) ^{2}}

= \frac{12 y}{( 2 x + 3 y ) ^{2}}

y^{^{'}} = - 0.000631594 \cdot y, y (0) = 30

n = 1 \sum \infty \frac{n}{n ^{2} + 25}

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

\frac{d}{d x} (lo g_{10} (2 x))

x \to 1.75 - lim (arcsin (\frac{x}{1.75}))

What is (\partial)/(\partial x)((6x-9y)/(6x+9y)) ?
The answer to (\partial)/(\partial x)((6x-9y)/(6x+9y)) is (12y)/((2x+3y)^2)