What is (\partial)/(\partial x)((y^2-x^2)/(xy)) ?

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

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(\partial)/(\partial x)((y^2-x^2)/(xy))

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

n = 1 \sum \infty \frac{4}{7 n + 2}

\frac{d}{d x} (x^{5} e^{- 3 x})

\frac{d}{d t} (7 e^{t} sin (t))

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

\frac{d}{d x} (1 + \frac{4}{x})

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