What is the d/(dy)(x/((x+y)^2)) ?

The d/(dy)(x/((x+y)^2)) is -(2x)/((x+y)^3)

What is the first d/(dy)(x/((x+y)^2)) ?

The first d/(dy)(x/((x+y)^2)) is -(2x)/((x+y)^3)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{5 - x}{x})

\int x^{3} - \frac{1}{x ^{2}} - x^{\frac{2}{3}} d x

x \to \infty lim (5 x^{2})

\int_{1}^{4} x - 1 d x

\frac{d}{d x} ((7)^{10 x + 1})

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