What is the d/(dy)(1/2 ln(x^2+y^2)) ?

The d/(dy)(1/2 ln(x^2+y^2)) is y/(x^2+y^2)

What is the first d/(dy)(1/2 ln(x^2+y^2)) ?

The first d/(dy)(1/2 ln(x^2+y^2)) is y/(x^2+y^2)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

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}) = 2 y

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

Simplify

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

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

n = 1 \sum \infty \frac{2 ^{n} x ^{2 n}}{3 ^{n + 1}}

\frac{\partial}{\partial x} (4 arctan (\frac{3}{x}))

f (x) = 4 + 5 x^{2}, (0, 4)

y^{^{''}} + 2 y^{^{'}} + 5 y = 8 sin (2 t)

\frac{\partial}{\partial x} (y cos (x) + 2 x e^{y})

What is the d/(dy)(1/2 ln(x^2+y^2)) ?
The d/(dy)(1/2 ln(x^2+y^2)) is y/(x^2+y^2)
What is the first d/(dy)(1/2 ln(x^2+y^2)) ?
The first d/(dy)(1/2 ln(x^2+y^2)) is y/(x^2+y^2)