What is (\partial)/(\partial y)((x^2)/(y^3)) ?

The answer to (\partial)/(\partial y)((x^2)/(y^3)) is -(3x^2)/(y^4)

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(\partial)/(\partial y)((x^2)/(y^3))

\frac{\partial}{\partial y} (\frac{x ^{2}}{y ^{3}})

- \frac{3 x ^{2}}{y ^{4}}

Solution steps

\frac{\partial}{\partial y} (\frac{x ^{2}}{y ^{3}})

Treat

x

as a constant

Take the constant out:

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

= x^{2} \frac{\partial}{\partial y} (\frac{1}{y ^{3}})

Apply exponent rule:

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

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

Apply the Power Rule:

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

= x^{2} (- 3 y^{- 3 - 1})

Simplify

x^{2} (- 3 y^{- 3 - 1}) : - \frac{3 x ^{2}}{y ^{4}}

= - \frac{3 x ^{2}}{y ^{4}}

\frac{\partial}{\partial θ} (r (θ) cos^{2} (θ))

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

\frac{d}{d x} (A x e^{- 3 x})

\int \frac{csc ( θ ) cot ( θ )}{5 - 4 csc ( θ )} d θ

f (x) = e^{6 x}

What is (\partial)/(\partial y)((x^2)/(y^3)) ?
The answer to (\partial)/(\partial y)((x^2)/(y^3)) is -(3x^2)/(y^4)