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

f (x) = cos (x) + 7

\frac{d}{d x} (arctan (2^{x}))

\int_{- \infty}^{0} e^{6 x} d x

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

\frac{d}{d x} (ln (5^{x}))

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