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

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

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))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d t} (\frac{ln ( 2 t - 1 )}{t ^{2} - 1})

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

\int (x^{2} - 6 x + 9) d x

\int \frac{2}{y ^{2}} d y

\int_{- 1}^{1} 1.5 x^{2} d x

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