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

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

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

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

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

- \frac{2 x}{y ^{3}}

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= x (- 2 y^{- 2 - 1})

Simplify

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

= - \frac{2 x}{y ^{3}}

n = 1 \sum \infty \frac{5}{n ( n + 6 )}

2 x^{2} + 3 x y + 1 y^{3} = - 10, (- 3, - 4)

x^{2} y^{^{''}} + x y^{^{'}} + y = sec (ln (x))

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

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