What is (\partial)/(\partial x)(5/(xy)) ?

The answer to (\partial)/(\partial x)(5/(xy)) is -5/(x^2y)

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(\partial)/(\partial x)(5/(xy))

\frac{\partial}{\partial x} (\frac{5}{x y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{5}{x y})

Treat

y

as a constant

Take the constant out:

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

= \frac{5}{y} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= \frac{5}{y} \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= \frac{5}{y} (- 1 \cdot x^{- 1 - 1})

Simplify

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

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

\int \frac{2 x ^{2}}{x ^{2} + 1} d x

x y^{^{'}} + y = x y^{2}

\frac{x}{e ^{x} - 1}, 1

\int (5 - 3 x^{2}) ln (x) d x

f (x) = arctan (x^{2})

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