What is (\partial)/(\partial x)(x^2+4y^2+3z^2) ?

The answer to (\partial)/(\partial x)(x^2+4y^2+3z^2) is 2x

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(\partial)/(\partial x)(x^2+4y^2+3z^2)

\frac{\partial}{\partial x} (x^{2} + 4 y^{2} + 3 z^{2})

2 x

Solution steps

\frac{\partial}{\partial x} (x^{2} + 4 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} (4 y^{2}) + \frac{\partial}{\partial x} (3 z^{2})

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

\frac{\partial}{\partial x} (4 y^{2}) = 0

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

= 2 x + 0 + 0

Simplify

= 2 x

y = 4 x^{2}, (- 1, 4)

x y^{^{'}} - 2 y = 2 x^{2} + 2 x + 1

(- 2, 0), (0, 1)

y^{^{'}} + \frac{3}{t ^{2}} y = 0

sin (6 (t - \frac{3 π}{6}))

What is (\partial)/(\partial x)(x^2+4y^2+3z^2) ?
The answer to (\partial)/(\partial x)(x^2+4y^2+3z^2) is 2x