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

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

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

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

\frac{1}{x - 6 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\int 2 cos (\frac{1}{2} x) d x

\frac{\partial}{\partial y} (4 x^{3} y^{2} - 2 x y^{3})

x^{3} + 7 e^{x}

\frac{x d y}{d x} = y^{2} - 4

\frac{d y}{d x} = (\frac{y}{x} + \frac{1}{4})^{2}

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