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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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