What is (\partial)/(\partial x)((y/(x-y))^6) ?

The answer to (\partial)/(\partial x)((y/(x-y))^6) is -(6y^6)/((x-y)^7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((y/(x-y))^6)

\frac{\partial}{\partial x} ((\frac{y}{x - y})^{6})

- \frac{6 y ^{6}}{( x - y ) ^{7}}

Solution steps

\frac{\partial}{\partial x} ((\frac{y}{x - y})^{6})

Treat

y

as a constant

Apply the chain rule:

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

= 6 (\frac{y}{x - y})^{5} \frac{\partial}{\partial x} (\frac{y}{x - y})

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

= 6 (\frac{y}{x - y})^{5} (- \frac{y}{( x - y ) ^{2}})

Simplify

6 (\frac{y}{x - y})^{5} (- \frac{y}{( x - y ) ^{2}}) : - \frac{6 y ^{6}}{( x - y ) ^{7}}

= - \frac{6 y ^{6}}{( x - y ) ^{7}}

x^{4^{x}}

\int 2 y^{2} cos (9 y) d y

y^{5} + 3 x^{2} y^{2} + 5 x^{4} = 49, (- 1, 2)

(- 5.3) (- 1.5)

What is (\partial)/(\partial x)((y/(x-y))^6) ?
The answer to (\partial)/(\partial x)((y/(x-y))^6) is -(6y^6)/((x-y)^7)