What is (\partial)/(\partial x)(x^2+2y^2+3z^2) ?

The answer to (\partial)/(\partial x)(x^2+2y^2+3z^2) is 2x

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(\partial)/(\partial x)(x^2+2y^2+3z^2)

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 3 z^{2})

2 x

Solution steps

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 3 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} (2 y^{2}) + \frac{\partial}{\partial x} (3 z^{2})

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

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

\frac{\partial}{\partial x} (3 z^{2}) = 0

= 2 x + 0 + 0

Simplify

= 2 x

y = 10 x, y = x^{2} - 11

\int x (2 x + 1) d x

\frac{\partial}{\partial y} (m sin (2 (m x + n y)))

y = \frac{1}{3 t}, (2, \frac{1}{6})

\int x \cdot cos^{2} (x) d x

What is (\partial)/(\partial x)(x^2+2y^2+3z^2) ?
The answer to (\partial)/(\partial x)(x^2+2y^2+3z^2) is 2x