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

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

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

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

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

Solution steps

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

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

f (x) = x^{2} \cdot ln (x)

\frac{d}{d x} (- \frac{6}{x})

\int_{- 5}^{5} e d x

x \to 4 lim (\frac{4 - x}{x - 4})

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

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