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

The answer to (\partial)/(\partial x)(4/(4x+y)) is -(16)/((4x+y)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- \frac{16}{( 4 x + y ) ^{2}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

4 (- \frac{1}{( 4 x + y ) ^{2}} \cdot 4) : - \frac{16}{( 4 x + y ) ^{2}}

= - \frac{16}{( 4 x + y ) ^{2}}

n = 1 \sum \infty \frac{2 n}{3}

\frac{\partial}{\partial x} (3 e^{y})

\frac{\partial}{\partial x} (sin (2 x) cos (2 t))

\int \frac{ln ( 2 x )}{ln ( 4 x ) x} d x

\frac{d}{d x} ((x + 6)^{7} (x + 3)^{5})

What is (\partial)/(\partial x)(4/(4x+y)) ?
The answer to (\partial)/(\partial x)(4/(4x+y)) is -(16)/((4x+y)^2)