What is the derivative of (3x-y)/(-x+y) ?

The derivative of (3x-y)/(-x+y) is (2y)/((-x+y)^2)

What is the first derivative of (3x-y)/(-x+y) ?

The first derivative of (3x-y)/(-x+y) is (2y)/((-x+y)^2)

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derivative of

\frac{3 x - y}{- x + y}

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

Solution steps

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

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

\frac{d}{d x} (- x + y) = - 1

= \frac{3 ( - x + y ) - ( - 1 ) ( 3 x - y )}{( - x + y ) ^{2}}

Simplify

\frac{3 ( - x + y ) - ( - 1 ) ( 3 x - y )}{( - x + y ) ^{2}} : \frac{2 y}{( - x + y ) ^{2}}

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

n = 0 \sum \infty \frac{1}{2 ^{n} + 1}

f (x) = \frac{7 x}{x - 1}, at x = 2

\int_{0}^{6} π (- x^{2} + 6 x)^{2} d x

\int x + 3 x^{2} d x

\int - \frac{x + 37}{4} d x

What is the derivative of (3x-y)/(-x+y) ?
The derivative of (3x-y)/(-x+y) is (2y)/((-x+y)^2)
What is the first derivative of (3x-y)/(-x+y) ?
The first derivative of (3x-y)/(-x+y) is (2y)/((-x+y)^2)