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

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

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

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

x (x^{3} z^{2} + 2 z)

Solution steps

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

Treat

x, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (2 yz) = 2 z

= x (x^{3} z^{2} + 2 z)

x \cdot (1 + x + 1 - x)

\frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) + C

\frac{27 \times ( s + 2 )}{2}

(2 + 4 i)^{4}

(y - x^{2}) (\frac{2 y ( y - x ^{2} )}{y ^{2} - x} - 1)

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