What is the d/(dy)((xy)/(x-y)) ?

The d/(dy)((xy)/(x-y)) is (x^2)/((x-y)^2)

What is the first d/(dy)((xy)/(x-y)) ?

The first d/(dy)((xy)/(x-y)) is (x^2)/((x-y)^2)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d y}{d y} = 1

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

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

Simplify

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

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

\int \frac{4 cosh ( 5 x )}{sinh ^{3} ( 5 x )} d x

f (x) = 3 x^{2} - 4 x + 5

\frac{d}{d x} (ln (tanh (2 x)))

y^{^{''}} - 3 y^{^{'}} - 4 y = 10 e^{- x} + 4 x + 3

\frac{d}{d x} ((5 x - 3) (2 x + 5)^{2})

What is the d/(dy)((xy)/(x-y)) ?
The d/(dy)((xy)/(x-y)) is (x^2)/((x-y)^2)
What is the first d/(dy)((xy)/(x-y)) ?
The first d/(dy)((xy)/(x-y)) is (x^2)/((x-y)^2)