What is the derivative of ln(x-4y) ?

The derivative of ln(x-4y) is (1-4\frac{dy)/(dx)}{x-4y}

What is the first derivative of ln(x-4y) ?

The first derivative of ln(x-4y) is (1-4\frac{dy)/(dx)}{x-4y}

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\frac{d}{d x} (ln (x - 4 y))

\frac{1 - 4 \frac{d y}{d x}}{x - 4 y}

Solution steps

\frac{d}{d x} (ln (x - 4 y))

Apply the chain rule:

\frac{1}{x - 4 y} \frac{d}{d x} (x - 4 y)

= \frac{1}{x - 4 y} \frac{d}{d x} (x - 4 y)

\frac{d}{d x} (x - 4 y) = 1 - 4 \frac{d y}{d x}

= \frac{1}{x - 4 y} (1 - 4 \frac{d y}{d x})

Simplify

\frac{1}{x - 4 y} (1 - 4 \frac{d y}{d x}) : \frac{1 - 4 \frac{d y}{d x}}{x - 4 y}

= \frac{1 - 4 \frac{d y}{d x}}{x - 4 y}

f (x) = (x^{3} + 3) e^{x}

\frac{1}{6} x^{2} - 3 x + 15

\int cos (y) cos (4 y) d y

2 x - x^{2}, - 3

\frac{d}{d x} (3 tan (x))

What is the derivative of ln(x-4y) ?
The derivative of ln(x-4y) is (1-4\frac{dy)/(dx)}{x-4y}
What is the first derivative of ln(x-4y) ?
The first derivative of ln(x-4y) is (1-4\frac{dy)/(dx)}{x-4y}