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

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

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

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

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

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

\int \frac{4 x ^{2} - 2}{x ^{3} - x} d x

\int x^{\frac{1}{3}} + 3 d x

\frac{\partial}{\partial x} (x sin (y) + z e^{x})

\int (6 x - 7) d x

f (x) = \frac{1 - 2 ln ( x )}{x ^{3}}

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