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

The derivative of ln(sqrt(x^2+y^2)) is x/(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/(x^2+y^2)

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derivative of

ln (x^{2} + y^{2})

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

Solution steps

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

Treat

y

as a constant

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}{x ^{2} + y ^{2}}

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

Simplify

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

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

\int \frac{( 2 - x ^{2} )}{x ^{3} + 3 x ^{2} + 2 x} d x

x \to + 4 lim (3 e^{1.7 x} + 1)

x^{3} + y^{3} = 12 x y - 8, (6, 4)

\frac{( s + 2 )}{( s ^{2} + 2 s + 2 )}

\int_{0}^{1} x \frac{2 ( x + 2 )}{5} d x

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