What is (\partial)/(\partial x)(ln(x-6y)-z) ?

The answer to (\partial)/(\partial x)(ln(x-6y)-z) is 1/(x-6y)

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(\partial)/(\partial x)(ln(x-6y)-z)

\frac{\partial}{\partial x} (ln (x - 6 y) - z)

\frac{1}{x - 6 y}

Solution steps

\frac{\partial}{\partial x} (ln (x - 6 y) - z)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (ln (x - 6 y)) - \frac{\partial}{\partial x} (z)

\frac{\partial}{\partial x} (ln (x - 6 y)) = \frac{1}{x - 6 y}

\frac{\partial}{\partial x} (z) = 0

= \frac{1}{x - 6 y} - 0

Simplify

= \frac{1}{x - 6 y}

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{3}})

\int \frac{1}{x ( ln ( x ^{2} ) ) ^{4}} d x

x \to 0 - lim (\frac{- ln ( 1 + 6 x )}{x})

\int 2 x (x^{2} + 7)^{6} d x

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

What is (\partial)/(\partial x)(ln(x-6y)-z) ?
The answer to (\partial)/(\partial x)(ln(x-6y)-z) is 1/(x-6y)