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

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

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

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

y^{2} z^{3}

Solution steps

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

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

\frac{\partial}{\partial x} (3 yz) = 0

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

Simplify

= y^{2} z^{3}

\frac{\partial}{\partial y} (x^{3} + y^{2} - 5 x y)

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

\frac{2 π r}{r}

\int \frac{( ln ( x ) ) ^{16}}{x} d x

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

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