What is (\partial)/(\partial x)(y+arctan(y/x)) ?

The answer to (\partial)/(\partial x)(y+arctan(y/x)) is -y/(y^2+x^2)

Popular >

(\partial)/(\partial x)(y+arctan(y/x))

\frac{\partial}{\partial x} (y + arctan (\frac{y}{x}))

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

Solution steps

\frac{\partial}{\partial x} (y + arctan (\frac{y}{x}))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (arctan (\frac{y}{x}))

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

\frac{\partial}{\partial x} (arctan (\frac{y}{x})) = - \frac{y}{y ^{2} + x ^{2}}

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

Simplify

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

\frac{\partial}{\partial y} (x^{3} - y^{2})

ln (6 x + 1)

x \to \infty lim (\frac{e ^{5 x - 3}}{ln ( x - 2 )})

f (x) = cos (a^{8} + x^{8})

x^{3} x

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