What is (\partial)/(\partial y)((x+4y+3z)^{3/2}) ?

The answer to (\partial)/(\partial y)((x+4y+3z)^{3/2}) is 6(x+4y+3z)^{1/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial y)((x+4y+3z)^{3/2})

\frac{\partial}{\partial y} ((x + 4 y + 3 z)^{\frac{3}{2}})

6 (x + 4 y + 3 z)^{\frac{1}{2}}

Solution steps

\frac{\partial}{\partial y} ((x + 4 y + 3 z)^{\frac{3}{2}})

Treat

x, z

as constants

Apply the chain rule:

\frac{3 ( x + 4 y + 3 z ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial y} (x + 4 y + 3 z)

= \frac{3 ( x + 4 y + 3 z ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial y} (x + 4 y + 3 z)

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

= \frac{3 ( x + 4 y + 3 z ) ^{\frac{1}{2}}}{2} \cdot 4

Simplify

\frac{3 ( x + 4 y + 3 z ) ^{\frac{1}{2}}}{2} \cdot 4 : 6 (x + 4 y + 3 z)^{\frac{1}{2}}

= 6 (x + 4 y + 3 z)^{\frac{1}{2}}

What is (\partial)/(\partial y)((x+4y+3z)^{3/2}) ?
The answer to (\partial)/(\partial y)((x+4y+3z)^{3/2}) is 6(x+4y+3z)^{1/2}