What is (\partial)/(\partial x)((y-2x)/(6y-x)) ?

The answer to (\partial)/(\partial x)((y-2x)/(6y-x)) is -(11y)/((6y-x)^2)

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(\partial)/(\partial x)((y-2x)/(6y-x))

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

- \frac{11 y}{( 6 y - x ) ^{2}}

Solution steps

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

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

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

\frac{\partial}{\partial x} (6 y - x) = - 1

= \frac{( - 2 ) ( 6 y - x ) - ( - 1 ) ( y - 2 x )}{( 6 y - x ) ^{2}}

Simplify

\frac{( - 2 ) ( 6 y - x ) - ( - 1 ) ( y - 2 x )}{( 6 y - x ) ^{2}} : - \frac{11 y}{( 6 y - x ) ^{2}}

= - \frac{11 y}{( 6 y - x ) ^{2}}

y = ln (x^{4} sin^{2} (x))

y^{^{'}} = \frac{1}{x}

\int - x e^{3 x} d x

\frac{\partial}{\partial x} (w)

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

What is (\partial)/(\partial x)((y-2x)/(6y-x)) ?
The answer to (\partial)/(\partial x)((y-2x)/(6y-x)) is -(11y)/((6y-x)^2)