What is (\partial)/(\partial x)(((3x-2y))/(3x+2y)) ?

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

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(\partial)/(\partial x)(((3x-2y))/(3x+2y))

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

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

Solution steps

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

\frac{\partial}{\partial x} (3 x - 2 y) = 3

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

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

Expand

3 (3 x + 2 y) - 3 (3 x - 2 y) : 12 y

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

\frac{x ^{2}}{x - 2}

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0

\frac{d y}{d x} = \frac{1 - y}{1 + x ^{2}}

- 2 x^{2}, at x = 1

y = sin (e^{x})

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