What is the d/(dy)(ln(sqrt(x^2+y^2))) ?

The d/(dy)(ln(sqrt(x^2+y^2))) is y/(x^2+y^2)

What is the first d/(dy)(ln(sqrt(x^2+y^2))) ?

The first d/(dy)(ln(sqrt(x^2+y^2))) is y/(x^2+y^2)

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = (x + y + 9)^{2}

\int_{- 2}^{3} \frac{25}{x ^{4}} d x

\int_{0}^{\infty} sin (4 x) d x

\int \frac{- 9}{x ^{2} + 16} d x

What is the d/(dy)(ln(sqrt(x^2+y^2))) ?
The d/(dy)(ln(sqrt(x^2+y^2))) is y/(x^2+y^2)
What is the first d/(dy)(ln(sqrt(x^2+y^2))) ?
The first d/(dy)(ln(sqrt(x^2+y^2))) is y/(x^2+y^2)