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

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

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

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

2 x

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

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

= 2 x + 0 + 0

Simplify

= 2 x

t \to 1 lim ((3 t - 1) (5 t^{2} + 2))

\frac{d}{d x} (sin (x) ln (9 x))

\frac{\partial}{\partial x} (e^{s i n^{2} (x)})

\int_{0}^{1} 3^{3 x} d x

\frac{1}{y ^{2}} - \frac{5}{y ^{4}} (y + 9 y^{3})

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