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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

f (x) = (x^{3} - 7) (3 x^{2} + 5)

x^{^{'}} = a x + b

\int x e^{\frac{- x}{4}} d x

\frac{d}{d x} (\frac{x ^{5} - 4 x ^{2}}{x ^{3}})

cos ((ln (x + 1))^{2} - e^{x^{2}})

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