What is (\partial)/(\partial x)((4x+3)/(4y+1)) ?

The answer to (\partial)/(\partial x)((4x+3)/(4y+1)) is 4/(4y+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)((4x+3)/(4y+1))

\frac{\partial}{\partial x} (\frac{4 x + 3}{4 y + 1})

\frac{4}{4 y + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{4 x + 3}{4 y + 1})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{4 y + 1} \frac{\partial}{\partial x} (4 x + 3)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{4 y + 1} (\frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (3))

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

\frac{\partial}{\partial x} (3) = 0

= \frac{1}{4 y + 1} (4 + 0)

Simplify

\frac{1}{4 y + 1} (4 + 0) : \frac{4}{4 y + 1}

= \frac{4}{4 y + 1}

What is (\partial)/(\partial x)((4x+3)/(4y+1)) ?
The answer to (\partial)/(\partial x)((4x+3)/(4y+1)) is 4/(4y+1)