What is (\partial)/(\partial x)((6x-8y)/(6x+8y)) ?

The answer to (\partial)/(\partial x)((6x-8y)/(6x+8y)) is (24y)/((3x+4y)^2)

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(\partial)/(\partial x)((6x-8y)/(6x+8y))

\frac{\partial}{\partial x} (\frac{6 x - 8 y}{6 x + 8 y})

\frac{24 y}{( 3 x + 4 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{6 x - 8 y}{6 x + 8 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 - 8 y ) ( 6 x + 8 y ) - \frac{\partial}{\partial x} ( 6 x + 8 y ) ( 6 x - 8 y )}{( 6 x + 8 y ) ^{2}}

\frac{\partial}{\partial x} (6 x - 8 y) = 6

\frac{\partial}{\partial x} (6 x + 8 y) = 6

= \frac{6 ( 6 x + 8 y ) - 6 ( 6 x - 8 y )}{( 6 x + 8 y ) ^{2}}

Simplify

\frac{6 ( 6 x + 8 y ) - 6 ( 6 x - 8 y )}{( 6 x + 8 y ) ^{2}} : \frac{24 y}{( 3 x + 4 y ) ^{2}}

= \frac{24 y}{( 3 x + 4 y ) ^{2}}

\frac{\partial}{\partial y} ((x^{2} + y^{2})^{\frac{1}{2}})

f (x) = x^{2} - 4

\int \frac{1}{x ^{2} ( x + 1 ) ^{2}} d x

x - 2

7 x - 4 x

What is (\partial)/(\partial x)((6x-8y)/(6x+8y)) ?
The answer to (\partial)/(\partial x)((6x-8y)/(6x+8y)) is (24y)/((3x+4y)^2)