What is (\partial)/(\partial y)(ln(sqrt(xy))) ?

The answer to (\partial)/(\partial y)(ln(sqrt(xy))) is 1/(2y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(ln(sqrt(xy)))

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

\frac{1}{2 y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{x y} \cdot \frac{1}{2 x y} x

Simplify

\frac{1}{x y} \cdot \frac{1}{2 x y} x : \frac{1}{2 y}

= \frac{1}{2 y}

\int (\frac{1}{x x ^{2} - 1}) d x

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 3 e^{- x}

\int - csc (2 w) cot (2 w) d w

\frac{d}{d θ} (cos (θ) - 2 sin (θ))

x \to 0 - lim (a x^{2} + \frac{b}{2})

What is (\partial)/(\partial y)(ln(sqrt(xy))) ?
The answer to (\partial)/(\partial y)(ln(sqrt(xy))) is 1/(2y)