What is (\partial)/(\partial x)(x/(x^2+y^2)+3x) ?

The answer to (\partial)/(\partial x)(x/(x^2+y^2)+3x) is (-x^2+y^2)/((x^2+y^2)^2)+3

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(\partial)/(\partial x)(x/(x^2+y^2)+3x)

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

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

Solution steps

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

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

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

x \to 5 lim ((6 + \frac{1}{x})^{2})

\int \frac{21}{x ln ( 8 x )} d x

y^{2} - 5 x = 1, x - y = 1

9 x^{2} + y^{2} = 9

What is (\partial)/(\partial x)(x/(x^2+y^2)+3x) ?
The answer to (\partial)/(\partial x)(x/(x^2+y^2)+3x) is (-x^2+y^2)/((x^2+y^2)^2)+3