What is (\partial)/(\partial x)(y/x) ?

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

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(\partial)/(\partial x)(y/x)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

= 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}}

\int \frac{1}{20 - x ^{2}} d x

\int \frac{2 ln ^{2} ( x ) + 16}{x} d x

\frac{d}{d y} (2)

\frac{\partial}{\partial x} (n y ln (n x))

\int 4 t + 2 d t

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