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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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