What is (\partial)/(\partial x)(x^{-3}y^{-4}) ?

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

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(\partial)/(\partial x)(x^{-3}y^{-4})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= y^{- 4} \frac{\partial}{\partial x} (x^{- 3})

Apply the Power Rule:

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

= y^{- 4} (- 3 x^{- 3 - 1})

Simplify

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

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

x, 0

(x + 4 y) d x + 2 x d y = 0

y = \frac{4}{1 + x ^{2}}

\frac{d ^{4} y}{d x ^{4}} + 3 y = 0

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