What is (\partial)/(\partial y)(x/(sqrt(y+z))) ?

The answer to (\partial)/(\partial y)(x/(sqrt(y+z))) is -x/(2(y+z)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(x/(sqrt(y+z)))

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (y + z) = 1

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

Simplify

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

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

\int_{0}^{1} \frac{3}{2 x - 5} d x

\int_{0}^{1} 19 \frac{1}{x ^{p}} d x

f (x) = 7 x^{6} e^{x} + e^{x} x^{7}

\frac{3}{s ( 6 s ^{2} + 5 s + 1 )}

\frac{\partial}{\partial y} (cos (x yz))

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