What is (\partial)/(\partial x)(-xy^2z^3-4xyz) ?

The answer to (\partial)/(\partial x)(-xy^2z^3-4xyz) is -y^2z^3-4yz

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(\partial)/(\partial x)(-xy^2z^3-4xyz)

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

- y^{2} z^{3} - 4 yz

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (4 x yz) = 4 yz

= - y^{2} z^{3} - 4 yz

n = 1 \sum \infty sin^{n} (2)

\int (x^{2} + 9)^{5} 2 x d x

y = e^{- 5 x}, x \geq 0

x \to 2 lim (4 x - 7)

\int \frac{1}{( z + \frac{1}{2} )} d z

What is (\partial)/(\partial x)(-xy^2z^3-4xyz) ?
The answer to (\partial)/(\partial x)(-xy^2z^3-4xyz) is -y^2z^3-4yz