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}}

t an g e n t f (x) = \frac{( x )}{x - 4}

\frac{\partial}{\partial x} (sin (x^{2} + 5))

(8 - r^{2}) d r = r^{3} sin (θ) d θ

\int_{0}^{1} \frac{x - 6}{x ^{2} - 6 x + 8} d x

3 x \frac{d y}{d x} = x^{2} - 4

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