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

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

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+z)))

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 4 x^{2} + 5 x - 3 d x

y = \frac{10}{1 + e ^{- x}}, (0, 5)

(3 x^{3} + 3) (x^{4} - 3 x)

\int_{0}^{5} x e^{- 4 x} d x

\int \frac{2}{9 - 4 x ^{2}} d x

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