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

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

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(\partial)/(\partial x)(sqrt(x^2+y^2)+1)

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

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

Solution steps

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

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} (1)

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

\frac{\partial}{\partial x} (1) = 0

= \frac{x}{x ^{2} + y ^{2}} + 0

Simplify

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

f (x) = \frac{x}{( x - 7 ) ^{2}}

\frac{( e ^{x} + e ^{- x} )}{2}

x \to 0 lim (\frac{x}{x + ∣ x ∣})

y = \frac{1}{18 x ^{2}}, y = x, y = \frac{x}{10}

\int \frac{x - 4}{x ^{2}} d x

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