What is (\partial)/(\partial x)(3/(3x+2y)) ?

The answer to (\partial)/(\partial x)(3/(3x+2y)) is -9/((3x+2y)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(3/(3x+2y))

\frac{\partial}{\partial x} (\frac{3}{3 x + 2 y})

- \frac{9}{( 3 x + 2 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{3}{3 x + 2 y})

Treat

y

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (\frac{1}{3 x + 2 y})

Apply exponent rule:

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

= 3 \frac{\partial}{\partial x} ((3 x + 2 y)^{- 1})

Apply the chain rule:

- \frac{1}{( 3 x + 2 y ) ^{2}} \frac{\partial}{\partial x} (3 x + 2 y)

= - \frac{1}{( 3 x + 2 y ) ^{2}} \frac{\partial}{\partial x} (3 x + 2 y)

\frac{\partial}{\partial x} (3 x + 2 y) = 3

= 3 (- \frac{1}{( 3 x + 2 y ) ^{2}} \cdot 3)

Simplify

3 (- \frac{1}{( 3 x + 2 y ) ^{2}} \cdot 3) : - \frac{9}{( 3 x + 2 y ) ^{2}}

= - \frac{9}{( 3 x + 2 y ) ^{2}}

What is (\partial)/(\partial x)(3/(3x+2y)) ?
The answer to (\partial)/(\partial x)(3/(3x+2y)) is -9/((3x+2y)^2)