What is the derivative of ln(2x-y) ?

The derivative of ln(2x-y) is (2-\frac{dy)/(dx)}{2x-y}

What is the first derivative of ln(2x-y) ?

The first derivative of ln(2x-y) is (2-\frac{dy)/(dx)}{2x-y}

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\frac{d}{d x} (ln (2 x - y))

\frac{2 - \frac{d y}{d x}}{2 x - y}

Solution steps

\frac{d}{d x} (ln (2 x - y))

Apply the chain rule:

\frac{1}{2 x - y} \frac{d}{d x} (2 x - y)

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

\frac{d}{d x} (2 x - y) = 2 - \frac{d y}{d x}

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

Simplify

\frac{1}{2 x - y} (2 - \frac{d y}{d x}) : \frac{2 - \frac{d y}{d x}}{2 x - y}

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

What is the derivative of ln(2x-y) ?
The derivative of ln(2x-y) is (2-\frac{dy)/(dx)}{2x-y}
What is the first derivative of ln(2x-y) ?
The first derivative of ln(2x-y) is (2-\frac{dy)/(dx)}{2x-y}