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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 + \frac{x}{x ^{2} + y ^{2}}

\frac{d}{d x} (4 x - 2)

\int \frac{x ^{3} + 4 x + 3}{x ^{4} + 5 x ^{2} + 4} d x

x y \frac{d y}{d x} = x^{2} + 8 y^{2}

\int (3 sec^{2} (x)) d x

\frac{\partial}{\partial y} (- 3 x e^{3 x y})

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