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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= - sin (\frac{y}{x}) \frac{1}{x}

Simplify

- sin (\frac{y}{x}) \frac{1}{x} : - \frac{sin ( \frac{y}{x} )}{x}

= - \frac{sin ( \frac{y}{x} )}{x}

X^{2} - 2 X - 15

\int 7 x^{4} d x

f (x) = 7 x^{2} + 5 x - 8

x \to 0 lim (\frac{3}{sin ( 3 x )})

e^{- x}

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