What is (\partial)/(\partial x)((9x-2y)/(9x+2y)) ?

The answer to (\partial)/(\partial x)((9x-2y)/(9x+2y)) is (36y)/((9x+2y)^2)

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(\partial)/(\partial x)((9x-2y)/(9x+2y))

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

\frac{36 y}{( 9 x + 2 y ) ^{2}}

Solution steps

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

\frac{\partial}{\partial x} (9 x - 2 y) = 9

\frac{\partial}{\partial x} (9 x + 2 y) = 9

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

Expand

9 (9 x + 2 y) - 9 (9 x - 2 y) : 36 y

= \frac{36 y}{( 9 x + 2 y ) ^{2}}

f (x) = \frac{x ^{\frac{1}{3}} - 4}{x ^{\frac{7}{2}}}

c \cdot sin (\frac{π x}{L})

\frac{3}{4} s^{2}

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

z \to 1 + i lim (z^{2} + i)

What is (\partial)/(\partial x)((9x-2y)/(9x+2y)) ?
The answer to (\partial)/(\partial x)((9x-2y)/(9x+2y)) is (36y)/((9x+2y)^2)