What is the derivative of ln(2xy+4) ?

The derivative of ln(2xy+4) is (x\frac{dy)/(dx)+y}{xy+2}

What is the first derivative of ln(2xy+4) ?

The first derivative of ln(2xy+4) is (x\frac{dy)/(dx)+y}{xy+2}

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\frac{d}{d x} (ln (2 x y + 4))

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

Solution steps

\frac{d}{d x} (ln (2 x y + 4))

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x y + 4} \cdot 2 (x \frac{d y}{d x} + y) : \frac{x \frac{d y}{d x} + y}{x y + 2}

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

What is the derivative of ln(2xy+4) ?
The derivative of ln(2xy+4) is (x\frac{dy)/(dx)+y}{xy+2}
What is the first derivative of ln(2xy+4) ?
The first derivative of ln(2xy+4) is (x\frac{dy)/(dx)+y}{xy+2}