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

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

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

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

4 sin (π t)

\int x^{3} - 3 x^{- 4} + 5 d x

\frac{d}{d x} (xx)

\int_{- 1}^{1} 6 - 6 x^{2} d x

\frac{d y}{d x} = 10 y e^{x + 6}

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