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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{3} - 12 x^{2} + 27 x, - x^{3} + 12 x^{2} - 27 x

\frac{d}{d x} (9 sin (x) + 9 cos (x))

x^{\frac{x}{3}}

f (x) = e^{2 x}, at x = \frac{1}{2} ln (2)

\frac{d}{d x} (x^{\frac{- 4}{3}})

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