What is (\partial)/(\partial x)(x^3yz^2+8yz) ?

The answer to (\partial)/(\partial x)(x^3yz^2+8yz) is 3x^2yz^2

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(\partial)/(\partial x)(x^3yz^2+8yz)

\frac{\partial}{\partial x} (x^{3} y z^{2} + 8 yz)

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

Solution steps

\frac{\partial}{\partial x} (x^{3} y z^{2} + 8 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} (8 yz)

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

\frac{\partial}{\partial x} (8 yz) = 0

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

Simplify

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

\int \frac{1}{cos ^{2} ( x ) + 5 cos ( x ) + 6} d x

\int 10 x^{3} + 2 x^{2} + \frac{1}{2} x + 3 d x

\frac{d y}{d x} = (y - 5)^{2}

\frac{d y}{d x}

\frac{- 14 x}{12 y}

What is (\partial)/(\partial x)(x^3yz^2+8yz) ?
The answer to (\partial)/(\partial x)(x^3yz^2+8yz) is 3x^2yz^2