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

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

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

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

\frac{6 y}{( 3 x + y ) ^{2}}

Solution steps

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

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

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

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

Expand

3 (3 x + y) - 3 (3 x - y) : 6 y

= \frac{6 y}{( 3 x + y ) ^{2}}

\int_{0}^{\frac{3 π}{2}} cos^{3} (5 x) d x

\int_{0}^{3} x^{2} + 9 d x

y = 2 x^{3} + 3 x^{2} - 12 x + 2

\int x^{2} - x - 6 d x

\frac{d}{d x} (4 sin (4 x))

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