What is the derivative of 2ln(xy) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

Simplify

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

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

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