What is (\partial)/(\partial y)(ln(y-3x)) ?

The answer to (\partial)/(\partial y)(ln(y-3x)) is 1/(y-3x)

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(\partial)/(\partial y)(ln(y-3x))

\frac{\partial}{\partial y} (ln (y - 3 x))

\frac{1}{y - 3 x}

Solution steps

\frac{\partial}{\partial y} (ln (y - 3 x))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{y - 3 x} \frac{\partial}{\partial y} (y - 3 x)

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

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

= \frac{1}{y - 3 x} \cdot 1

Simplify

= \frac{1}{y - 3 x}

\int - 24 t e^{- 3 t} d t

\int \frac{x ^{2} - x + 2}{x ^{4} + 4 x ^{2} + 3} d x

\int i n^{2} x d x

y = x^{2} - x + 10, at x = 3

What is (\partial)/(\partial y)(ln(y-3x)) ?
The answer to (\partial)/(\partial y)(ln(y-3x)) is 1/(y-3x)