What is (\partial)/(\partial y)(x^{-2}y^{-5}) ?

The answer to (\partial)/(\partial y)(x^{-2}y^{-5}) is -5/(x^2y^6)

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(\partial)/(\partial y)(x^{-2}y^{-5})

\frac{\partial}{\partial y} (x^{- 2} y^{- 5})

- \frac{5}{x ^{2} y ^{6}}

Solution steps

\frac{\partial}{\partial y} (x^{- 2} y^{- 5})

Treat

x

as a constant

Take the constant out:

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

= x^{- 2} \frac{\partial}{\partial y} (y^{- 5})

Apply the Power Rule:

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

= x^{- 2} (- 5 y^{- 5 - 1})

Simplify

x^{- 2} (- 5 y^{- 5 - 1}) : - \frac{5}{x ^{2} y ^{6}}

= - \frac{5}{x ^{2} y ^{6}}

\int sin (14 x) cos (9 x) d x

\frac{d}{d x} (sin (\frac{2}{x}))

\frac{d x}{d y} = \frac{y}{5}

\frac{\partial}{\partial x} (3 x e^{x})

x \to 3 lim (2)

What is (\partial)/(\partial y)(x^{-2}y^{-5}) ?
The answer to (\partial)/(\partial y)(x^{-2}y^{-5}) is -5/(x^2y^6)