What is (\partial)/(\partial x)(2x^2+3y^2+5z^2) ?

The answer to (\partial)/(\partial x)(2x^2+3y^2+5z^2) is 4x

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(\partial)/(\partial x)(2x^2+3y^2+5z^2)

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2} + 5 z^{2})

4 x

Solution steps

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2} + 5 z^{2})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{2}) + \frac{\partial}{\partial x} (3 y^{2}) + \frac{\partial}{\partial x} (5 z^{2})

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

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

\frac{\partial}{\partial x} (5 z^{2}) = 0

= 4 x + 0 + 0

Simplify

= 4 x

What is (\partial)/(\partial x)(2x^2+3y^2+5z^2) ?
The answer to (\partial)/(\partial x)(2x^2+3y^2+5z^2) is 4x