What is (\partial)/(\partial x)((sqrt(y))/(2sqrt(x))) ?

The answer to (\partial)/(\partial x)((sqrt(y))/(2sqrt(x))) is -(sqrt(y))/(4x^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((sqrt(y))/(2sqrt(x)))

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

- \frac{y}{4 x ^{\frac{3}{2}}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= \frac{y}{2} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

\frac{y}{2} (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{y}{4 x ^{\frac{3}{2}}}

= - \frac{y}{4 x ^{\frac{3}{2}}}

\int (3 x + 1)^{2} d x

t^{2} y^{^{'}} + t y = 3, y (1) = 6

f (x) = 9 x

y = - x, y = \frac{1}{2} x - \frac{3}{2}, x = - 1, x = 3

\frac{x ^{2}}{( 3 + x )}

What is (\partial)/(\partial x)((sqrt(y))/(2sqrt(x))) ?
The answer to (\partial)/(\partial x)((sqrt(y))/(2sqrt(x))) is -(sqrt(y))/(4x^{3/2)}