What is (\partial)/(\partial x)(x^2+(y-1)^2+z^2) ?

The answer to (\partial)/(\partial x)(x^2+(y-1)^2+z^2) is 2x

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(\partial)/(\partial x)(x^2+(y-1)^2+z^2)

\frac{\partial}{\partial x} (x^{2} + (y - 1)^{2} + z^{2})

2 x

Solution steps

\frac{\partial}{\partial x} (x^{2} + (y - 1)^{2} + z^{2})

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 - 1)^{2}) + \frac{\partial}{\partial x} (z^{2})

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

\frac{\partial}{\partial x} ((y - 1)^{2}) = 0

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

= 2 x + 0 + 0

Simplify

= 2 x

x, x^{2.42}, [0.99, 1]

\frac{d}{d x} (\frac{2 x}{x + 8})

y = 5 csc (x) + 6 cos (x)

y = sin (x), y = 5 x, x = \frac{π}{2}, x = π

\int \frac{1}{2 x + 3 + x} d x

What is (\partial)/(\partial x)(x^2+(y-1)^2+z^2) ?
The answer to (\partial)/(\partial x)(x^2+(y-1)^2+z^2) is 2x