What is (\partial)/(\partial y)(x/y) ?

The answer to (\partial)/(\partial y)(x/y) is -x/(y^2)

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(\partial)/(\partial y)(x/y)

\frac{\partial}{\partial y} (\frac{x}{y})

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

Solution steps

\frac{\partial}{\partial y} (\frac{x}{y})

Treat

x

as a constant

Take the constant out:

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

= x \frac{\partial}{\partial y} (\frac{1}{y})

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d x} (e^{a x^{8}})

f (x) = - \frac{4 x}{x ^{2} + 1}, at x = - 1

t \to 0 lim (\frac{t ^{3} - 3 t}{t})

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

\frac{\partial}{\partial y} (10 x^{\frac{1}{4}} y^{\frac{3}{4}})

What is (\partial)/(\partial y)(x/y) ?
The answer to (\partial)/(\partial y)(x/y) is -x/(y^2)