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

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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to \infty lim (2^{x} + 1)

x \to - 2 lim (f (x))

\int_{- 3}^{3} x^{2} - 9 d x

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

y = \frac{2 ^{x}}{2} + \frac{12}{x}

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