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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int 1 + y^{2} d y

\int_{- 1}^{2} 4 x^{3} - 3 x^{2} d x

\int sin (3 x) + e^{2 x} d x

\int (\frac{x sin ^{2} ( x )}{2}) d x

x \to 0 + lim (x^{(x^{2})})

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