What is (\partial)/(\partial x)(x^3yz^2+4yz) ?

The answer to (\partial)/(\partial x)(x^3yz^2+4yz) is 3x^2yz^2

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(\partial)/(\partial x)(x^3yz^2+4yz)

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (4 yz) = 0

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

Simplify

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

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\frac{d}{d x} (6 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

5 x^{^{''}} + 5 x^{^{'}} + 6 x = 0, x^{^{'}} (0) = 0.45, x (0) = - 0.3

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

What is (\partial)/(\partial x)(x^3yz^2+4yz) ?
The answer to (\partial)/(\partial x)(x^3yz^2+4yz) is 3x^2yz^2