What is (\partial)/(\partial y)(x^5yz^2+4yz) ?

The answer to (\partial)/(\partial y)(x^5yz^2+4yz) is x^5z^2+4z

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(\partial)/(\partial y)(x^5yz^2+4yz)

\frac{\partial}{\partial y} (x^{5} y z^{2} + 4 yz)

x^{5} z^{2} + 4 z

Solution steps

\frac{\partial}{\partial y} (x^{5} y z^{2} + 4 yz)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{5} y z^{2}) + \frac{\partial}{\partial y} (4 yz)

\frac{\partial}{\partial y} (x^{5} y z^{2}) = x^{5} z^{2}

\frac{\partial}{\partial y} (4 yz) = 4 z

= x^{5} z^{2} + 4 z

f (x) = x^{2} + x, at a = 5

\frac{d}{d x} (I n x y (I, x)^{2})

\int \frac{13}{x ( x ^{2} + 4 ) ^{2}} d x

y = 38 x - 16 x^{2}, at x = 1

\int \frac{16}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

What is (\partial)/(\partial y)(x^5yz^2+4yz) ?
The answer to (\partial)/(\partial y)(x^5yz^2+4yz) is x^5z^2+4z