What is (\partial)/(\partial x)(9/(8x+3y)) ?

The answer to (\partial)/(\partial x)(9/(8x+3y)) is -(72)/((8x+3y)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(9/(8x+3y))

\frac{\partial}{\partial x} (\frac{9}{8 x + 3 y})

- \frac{72}{( 8 x + 3 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{9}{8 x + 3 y})

Treat

y

as a constant

Take the constant out:

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

= 9 \frac{\partial}{\partial x} (\frac{1}{8 x + 3 y})

Apply exponent rule:

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

= 9 \frac{\partial}{\partial x} ((8 x + 3 y)^{- 1})

Apply the chain rule:

- \frac{1}{( 8 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (8 x + 3 y)

= - \frac{1}{( 8 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (8 x + 3 y)

\frac{\partial}{\partial x} (8 x + 3 y) = 8

= 9 (- \frac{1}{( 8 x + 3 y ) ^{2}} \cdot 8)

Simplify

9 (- \frac{1}{( 8 x + 3 y ) ^{2}} \cdot 8) : - \frac{72}{( 8 x + 3 y ) ^{2}}

= - \frac{72}{( 8 x + 3 y ) ^{2}}

\int \frac{x}{1 - 4 x ^{2}} d x

2^{x} lo g_{2} (x)

\int \frac{3 x - 1}{x + 1} d x

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

\int_{1}^{3} 3 x^{2} + \frac{1}{12 x ^{2}} d x

What is (\partial)/(\partial x)(9/(8x+3y)) ?
The answer to (\partial)/(\partial x)(9/(8x+3y)) is -(72)/((8x+3y)^2)