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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

x \to 0 lim (\frac{( sin ( 5 x ) )}{x})

\int \frac{cos ( t )}{t} d t

\frac{d y}{d x} = x (y - 1)^{2}

y = (x^{3} - 16 x)^{10}, (4, 0)

x \to 0 lim (e^{x} - \frac{1}{x})

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