What is (\partial)/(\partial y)((4x-4z)/(y+4z)) ?

The answer to (\partial)/(\partial y)((4x-4z)/(y+4z)) is -(4x-4z)/((y+4z)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)((4x-4z)/(y+4z))

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

= (4 x - 4 z) \frac{\partial}{\partial y} (\frac{1}{y + 4 z})

Apply exponent rule:

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

= (4 x - 4 z) \frac{\partial}{\partial y} ((y + 4 z)^{- 1})

Apply the chain rule:

- \frac{1}{( y + 4 z ) ^{2}} \frac{\partial}{\partial y} (y + 4 z)

= - \frac{1}{( y + 4 z ) ^{2}} \frac{\partial}{\partial y} (y + 4 z)

\frac{\partial}{\partial y} (y + 4 z) = 1

= (4 x - 4 z) (- \frac{1}{( y + 4 z ) ^{2}} \cdot 1)

Simplify

(4 x - 4 z) (- \frac{1}{( y + 4 z ) ^{2}} \cdot 1) : - \frac{4 x - 4 z}{( y + 4 z ) ^{2}}

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

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

\int \frac{r}{a ^{2} - r ^{2}} d r

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

\frac{d}{d x} (\frac{1}{10} (x - 60)^{2} + 100)

- 7 x^{2}

What is (\partial)/(\partial y)((4x-4z)/(y+4z)) ?
The answer to (\partial)/(\partial y)((4x-4z)/(y+4z)) is -(4x-4z)/((y+4z)^2)