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

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

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(\partial)/(\partial x)(x^3z+z^3x-2yz)

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

z^{3} + 3 x^{2} z

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (2 yz) = 0

= 3 z x^{2} + z^{3} - 0

Simplify

= z^{3} + 3 x^{2} z

f (x) = x^{2} x^{3} + 1, at x = 1

x \to 1 lim (x^{2} + 3 x - 2)

\int_{0}^{1} x \cdot e^{- x} d x

\int_{0}^{1} (e^{- x}) d x

f (x) = x^{2} (1 - 9 x)

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