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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{- 1}^{1} sec^{3} (x) d x

f (x) = \frac{( 2 x + 1 )}{x + 2}, at x = 1

y = \frac{3 x - 4}{2 x + 3}

\frac{\partial}{\partial x} (x^{6} y^{6} + 9 x^{4} y)

\frac{d}{d x} ((4 x^{3} + 5 x^{2}) (9 x))

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