What is (\partial)/(\partial x)(ln((3xy)/(5z))) ?

The answer to (\partial)/(\partial x)(ln((3xy)/(5z))) is 1/x

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(\partial)/(\partial x)(ln((3xy)/(5z)))

\frac{\partial}{\partial x} (ln (\frac{3 x y}{5 z}))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{3 x y}{5 z}))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{\frac{3 x y}{5 z}} \frac{\partial}{\partial x} (\frac{3 x y}{5 z})

= \frac{1}{\frac{3 x y}{5 z}} \frac{\partial}{\partial x} (\frac{3 x y}{5 z})

\frac{\partial}{\partial x} (\frac{3 x y}{5 z}) = \frac{3 y}{5 z}

= \frac{1}{\frac{3 x y}{5 z}} \cdot \frac{3 y}{5 z}

Simplify

\frac{1}{\frac{3 x y}{5 z}} \cdot \frac{3 y}{5 z} : \frac{1}{x}

= \frac{1}{x}

\int (2 x + 1) x - 5 d x

∣ 4 x - 1 ∣, x^{2} - 5

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

x \to 4 lim (7)

x \to 0 lim (\frac{1}{8} + x - (\frac{1}{8}))

What is (\partial)/(\partial x)(ln((3xy)/(5z))) ?
The answer to (\partial)/(\partial x)(ln((3xy)/(5z))) is 1/x