What is (\partial)/(\partial y)(x+1/2 ln(x^2+y^2)) ?

The answer to (\partial)/(\partial y)(x+1/2 ln(x^2+y^2)) is y/(x^2+y^2)

Popular >

(\partial)/(\partial y)(x+1/2 ln(x^2+y^2))

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x) = 0

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

= 0 + \frac{y}{x ^{2} + y ^{2}}

Simplify

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

\frac{1}{y}

x \to 1 lim (\frac{e ^{x}}{2})

f (x) = cos (x^{5})

\frac{\partial}{\partial x} (p (x)^{2})

y = \frac{x}{5}, y = 1, x = 0

What is (\partial)/(\partial y)(x+1/2 ln(x^2+y^2)) ?
The answer to (\partial)/(\partial y)(x+1/2 ln(x^2+y^2)) is y/(x^2+y^2)