What is (\partial}{\partial x}(ln(\frac{2xy)/z)) ?

The answer to (\partial}{\partial x}(ln(\frac{2xy)/z)) is 1/x

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(\partial}{\partial x}(ln(\frac{2xy)/z))

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

\frac{1}{x}

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

\int \frac{5 x}{3 x ^{\frac{1}{3}}} d x

y = 1.1 x + e^{x}, (0, 1)

y = 0, y = x^{2}, y = 4 x - x^{2}, [0, 2]

(1 + cos (t)) y^{^{'}} = (1 + e^{- y}) sin (t), y (0) = 0

What is (\partial}{\partial x}(ln(\frac{2xy)/z)) ?
The answer to (\partial}{\partial x}(ln(\frac{2xy)/z)) is 1/x