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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int (7^{x} - sec^{2} (x)) d x

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

x \to 5 + lim (x - 5)

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