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

The answer to (\partial)/(\partial x)(z^2+5x^2+y^2) is 10x

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

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

10 x

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

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

= 0 + 10 x + 0

Simplify

= 10 x

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What is (\partial)/(\partial x)(z^2+5x^2+y^2) ?
The answer to (\partial)/(\partial x)(z^2+5x^2+y^2) is 10x