What is (\partial}{\partial y}(sin(\frac{5x)/y)) ?

The answer to (\partial}{\partial y}(sin(\frac{5x)/y)) is -(5xcos((5x)/y))/(y^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial}{\partial y}(sin(\frac{5x)/y))

\frac{\partial}{\partial y} (sin (\frac{5 x}{y}))

- \frac{5 x cos ( \frac{5 x}{y} )}{y ^{2}}

Solution steps

\frac{\partial}{\partial y} (sin (\frac{5 x}{y}))

Treat

x

as a constant

Apply the chain rule:

cos (\frac{5 x}{y}) \frac{\partial}{\partial y} (\frac{5 x}{y})

= cos (\frac{5 x}{y}) \frac{\partial}{\partial y} (\frac{5 x}{y})

\frac{\partial}{\partial y} (\frac{5 x}{y}) = - \frac{5 x}{y ^{2}}

= cos (\frac{5 x}{y}) (- \frac{5 x}{y ^{2}})

Simplify

cos (\frac{5 x}{y}) (- \frac{5 x}{y ^{2}}) : - \frac{5 x cos ( \frac{5 x}{y} )}{y ^{2}}

= - \frac{5 x cos ( \frac{5 x}{y} )}{y ^{2}}

What is (\partial}{\partial y}(sin(\frac{5x)/y)) ?
The answer to (\partial}{\partial y}(sin(\frac{5x)/y)) is -(5xcos((5x)/y))/(y^2)