What is (\partial)/(\partial x)(1/(xy)) ?

The answer to (\partial)/(\partial x)(1/(xy)) is -1/(x^2y)

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(\partial)/(\partial x)(1/(xy))

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

- \frac{1}{x ^{2} y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{1}{x ^{2} y}

\int e^{3 - 4 x} d x

7 y^{^{''}} + 13 y^{^{'}} - 2 y = 0

x \to (\frac{π}{2}) + lim (6 e^{t a n (x)})

2 t^{- \frac{1}{4}}

x^{\frac{1}{3}} - x^{\frac{1}{2}}, [1, 27]

What is (\partial)/(\partial x)(1/(xy)) ?
The answer to (\partial)/(\partial x)(1/(xy)) is -1/(x^2y)