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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

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

\int 5 x arctan (x) d x

\frac{\partial}{\partial y} ((e^{x} - 4 x) cos (y))

\int \frac{1}{x} + \frac{y ^{2}}{x ^{2}} d x

\frac{d}{d x} (ln ((x - 1)^{3} (x^{2} + 1)^{4}))

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