What is (\partial)/(\partial z)(((x+y))/((y+z))) ?

The answer to (\partial)/(\partial z)(((x+y))/((y+z))) is -(x+y)/((y+z)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial z)(((x+y))/((y+z)))

\frac{\partial}{\partial z} (\frac{( x + y )}{( y + z )})

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

Solution steps

\frac{\partial}{\partial z} (\frac{( x + y )}{( y + z )})

Treat

x, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= (x + y) \frac{\partial}{\partial z} ((y + z)^{- 1})

Apply the chain rule:

- \frac{1}{( y + z ) ^{2}} \frac{\partial}{\partial z} (y + z)

= - \frac{1}{( y + z ) ^{2}} \frac{\partial}{\partial z} (y + z)

\frac{\partial}{\partial z} (y + z) = 1

= (x + y) (- \frac{1}{( y + z ) ^{2}} \cdot 1)

Simplify

(x + y) (- \frac{1}{( y + z ) ^{2}} \cdot 1) : - \frac{x + y}{( y + z ) ^{2}}

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

\int \frac{e ^{θ}}{a + b e ^{θ}} d θ

\int 4 - 3 (1 + x^{2})^{- 1} d x

\int \frac{6 ( 1 + x )}{x ( x ^{2} + 7 x + 6 )} d x

\frac{\partial}{\partial x} (cos^{4} (x^{3} y^{5}))

x \to - 8 lim (x^{2} - 3)

What is (\partial)/(\partial z)(((x+y))/((y+z))) ?
The answer to (\partial)/(\partial z)(((x+y))/((y+z))) is -(x+y)/((y+z)^2)