What is the d/(dy)(sqrt((w(x+y))/(xy))) ?

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

What is the first d/(dy)(sqrt((w(x+y))/(xy))) ?

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

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\frac{d}{d y} (\frac{w ( x + y )}{x y})

- \frac{w x y}{2 y ^{2} x + y}

Solution steps

\frac{d}{d y} (\frac{w ( x + y )}{x y})

Treat

w, x

as constants

Apply the chain rule:

\frac{1}{2 \frac{w ( x + y )}{x y}} \frac{d}{d y} (\frac{w ( x + y )}{x y})

= \frac{1}{2 \frac{w ( x + y )}{x y}} \frac{d}{d y} (\frac{w ( x + y )}{x y})

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

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

Simplify

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

= - \frac{w x y}{2 y ^{2} x + y}

\int_{1}^{4} \frac{x ^{2} + 4}{5 x - x ^{2}} d x

\frac{d}{d x} ((- 2 x^{2} + 2 x + 3) (- x^{2} - 3 x - 4))

\frac{d}{d x} (\frac{d y}{d x}) + 81 y = 0

\int cos (\frac{u}{v}) d u

x \to + 0 lim (\frac{sin ( 0 )}{0})

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