What is (\partial)/(\partial x)((5x+4y)/(4x-y)) ?

The answer to (\partial)/(\partial x)((5x+4y)/(4x-y)) is -(21y)/((4x-y)^2)

Popular >

(\partial)/(\partial x)((5x+4y)/(4x-y))

\frac{\partial}{\partial x} (\frac{5 x + 4 y}{4 x - y})

- \frac{21 y}{( 4 x - y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{5 x + 4 y}{4 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} ( 5 x + 4 y ) ( 4 x - y ) - \frac{\partial}{\partial x} ( 4 x - y ) ( 5 x + 4 y )}{( 4 x - y ) ^{2}}

\frac{\partial}{\partial x} (5 x + 4 y) = 5

\frac{\partial}{\partial x} (4 x - y) = 4

= \frac{5 ( 4 x - y ) - 4 ( 5 x + 4 y )}{( 4 x - y ) ^{2}}

Simplify

\frac{5 ( 4 x - y ) - 4 ( 5 x + 4 y )}{( 4 x - y ) ^{2}} : - \frac{21 y}{( 4 x - y ) ^{2}}

= - \frac{21 y}{( 4 x - y ) ^{2}}

\int_{(1 - x)^{2}}^{(1 + x)^{2}} \int_{1}^{3} y e^{x^{2}} d x d y

x \to - 4 - lim (\frac{3 - 8 x}{x + 4})

\frac{d y}{d x}, 2 (x^{2} + y^{2}) 2 = 81 (x^{2} - y^{2})

\frac{d}{d x} (\frac{x ^{2}}{2} + x \cdot (ln (x) - 1))

x \to 3 lim (4 x^{3} - 2 x^{2} + x - 6)

What is (\partial)/(\partial x)((5x+4y)/(4x-y)) ?
The answer to (\partial)/(\partial x)((5x+4y)/(4x-y)) is -(21y)/((4x-y)^2)