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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (2 x) = 2

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

\int \frac{4}{x} + \frac{x}{x ^{2} + 5} d x

t an g e n t y = 3 - 9 x^{2}

im pl i c i t \frac{d y}{d x}, e^{x} y = 8

y^{^{'}} = \frac{( x ^{2} y + y ^{3} )}{x ^{3}}

\int_{1}^{5} \frac{ln ( x )}{x ^{3}} d x

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