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

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

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

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

2 x

Solution steps

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

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

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

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

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

= 2 x + 0 + 0

Simplify

= 2 x

\int \frac{2}{3} e^{3 x} x d x

\frac{d}{d x} (x^{4} + 5 x)

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

x^{5} + 1

10 y^{^{''}} + 1000 y = 170 cos (8 t)

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