What is (\partial)/(\partial x)(yx^{-1}) ?

The answer to (\partial)/(\partial x)(yx^{-1}) is -y/(x^2)

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(\partial)/(\partial x)(yx^{-1})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{( x ^{2} + 1 ) d y}{d x} + 6 x (y - 1) = 0, y (0) = 6

\int \frac{1}{x ^{3}} ln (x) d x

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

\int (3 - \frac{2}{x ^{3}} + \frac{1}{x}) d x

\int_{0}^{1} 2 x 1 + 4 x^{2} d x

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