What is (\partial}{\partial x}(ln(\frac{xy)/z)) ?

The answer to (\partial}{\partial x}(ln(\frac{xy)/z)) is 1/x

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(\partial}{\partial x}(ln(\frac{xy)/z))

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

\frac{1}{x}

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

\int (e^{2 x} + e^{- 2 x})^{2} d x

x \to 0 lim (arccos (x^{2}))

\int (1 - \frac{3}{x} + y) d x

\frac{d y}{d t} = 0.07 y + 200

x \to \infty lim (- 8 x^{6})

What is (\partial}{\partial x}(ln(\frac{xy)/z)) ?
The answer to (\partial}{\partial x}(ln(\frac{xy)/z)) is 1/x