What is (\partial)/(\partial x)(sqrt(xx+yy)) ?

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

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(\partial)/(\partial x)(sqrt(xx+yy))

\frac{\partial}{\partial x} (xx + yy)

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

Solution steps

\frac{\partial}{\partial x} (xx + yy)

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 xx + yy} \frac{\partial}{\partial x} (xx + yy)

= \frac{1}{2 xx + yy} \frac{\partial}{\partial x} (xx + yy)

\frac{\partial}{\partial x} (xx + yy) = 2 x

= \frac{1}{2 xx + yy} \cdot 2 x

Simplify

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

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

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