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

The answer to (\partial)/(\partial y)(sin(y/x)) is (cos(y/x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

cos (\frac{y}{x}) \frac{1}{x} : \frac{cos ( \frac{y}{x} )}{x}

= \frac{cos ( \frac{y}{x} )}{x}

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

(3 x^{2} + 2 x), at (a = - 3)

y = x, y = x - 2, [0, 4]

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} - 3 z^{2} - 11)

\int (cos (t)) d t

What is (\partial)/(\partial y)(sin(y/x)) ?
The answer to (\partial)/(\partial y)(sin(y/x)) is (cos(y/x))/x