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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{1}{k} - \frac{1}{k + 1}

4 (2 y + 3)

(x^{2} + 4 x + 5)^{2}

(x - 10)^{2}

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