What is the derivative of sqrt(x^2+y^2) ?

The derivative of sqrt(x^2+y^2) is x/(sqrt(x^2+y^2))

What is the first derivative of sqrt(x^2+y^2) ?

The first derivative of sqrt(x^2+y^2) is x/(sqrt(x^2+y^2))

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derivative of

x^{2} + y^{2}

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{d}{d 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}}

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What is the derivative of sqrt(x^2+y^2) ?
The derivative of sqrt(x^2+y^2) is x/(sqrt(x^2+y^2))
What is the first derivative of sqrt(x^2+y^2) ?
The first derivative of sqrt(x^2+y^2) is x/(sqrt(x^2+y^2))