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

The derivative of ln(x-y) is (1-\frac{dy)/(dx)}{x-y}

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

The first derivative of ln(x-y) is (1-\frac{dy)/(dx)}{x-y}

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

\frac{1 - \frac{d y}{d x}}{x - y}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{x \cdot y}{x ^{2} + y ^{2}})

\int x (sin (x) - cos (x^{2})) d x

y^{^{''}} + 4 y = 3 sin (x)

\frac{d V}{12 - 2 V} = d t, V (0) = 1

What is the derivative of ln(x-y) ?
The derivative of ln(x-y) is (1-\frac{dy)/(dx)}{x-y}
What is the first derivative of ln(x-y) ?
The first derivative of ln(x-y) is (1-\frac{dy)/(dx)}{x-y}