What is (\partial)/(\partial x)((6x-7y)/(6x+7y)) ?

The answer to (\partial)/(\partial x)((6x-7y)/(6x+7y)) is (84y)/((6x+7y)^2)

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(\partial)/(\partial x)((6x-7y)/(6x+7y))

\frac{\partial}{\partial x} (\frac{6 x - 7 y}{6 x + 7 y})

\frac{84 y}{( 6 x + 7 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{6 x - 7 y}{6 x + 7 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 - 7 y ) ( 6 x + 7 y ) - \frac{\partial}{\partial x} ( 6 x + 7 y ) ( 6 x - 7 y )}{( 6 x + 7 y ) ^{2}}

\frac{\partial}{\partial x} (6 x - 7 y) = 6

\frac{\partial}{\partial x} (6 x + 7 y) = 6

= \frac{6 ( 6 x + 7 y ) - 6 ( 6 x - 7 y )}{( 6 x + 7 y ) ^{2}}

Expand

6 (6 x + 7 y) - 6 (6 x - 7 y) : 84 y

= \frac{84 y}{( 6 x + 7 y ) ^{2}}

y = 2 (1.1)^{t}

y = 12 x, (9, 36)

5 y^{^{''}} + 25 y^{^{'}} + 1700 y = 10 sin (20 t)

x (3 x - 1)

2 x (x^{2} + 1)

What is (\partial)/(\partial x)((6x-7y)/(6x+7y)) ?
The answer to (\partial)/(\partial x)((6x-7y)/(6x+7y)) is (84y)/((6x+7y)^2)