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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

x \to 3 lim (π)

x y^{^{'}} + 2 y = 5 x

\frac{\partial}{\partial x} (\frac{t}{x + 1})

\int_{- 2 π}^{π} sin^{2} (x) d x

x \to 3 lim (\frac{ln ( x ) - ln ( 3 )}{x - 3})

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