What is (\partial)/(\partial y)(x^2y+yz^3+z^5x) ?

The answer to (\partial)/(\partial y)(x^2y+yz^3+z^5x) is x^2+z^3

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(\partial)/(\partial y)(x^2y+yz^3+z^5x)

\frac{\partial}{\partial y} (x^{2} y + y z^{3} + z^{5} x)

x^{2} + z^{3}

Solution steps

\frac{\partial}{\partial y} (x^{2} y + y z^{3} + z^{5} x)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{2} y) + \frac{\partial}{\partial y} (y z^{3}) + \frac{\partial}{\partial y} (z^{5} x)

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

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

\frac{\partial}{\partial y} (z^{5} x) = 0

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

Simplify

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

\frac{d}{d x} ((x + \frac{1}{x}) (x - \frac{1}{x}))

y^{^{''}} + 10 y^{^{'}} + 25 = 0

\int (\frac{100}{25 + ( 5 y ) ^{2}} + e^{4}) d y

\int \frac{x ^{2}}{( x - 1 )} d x

What is (\partial)/(\partial y)(x^2y+yz^3+z^5x) ?
The answer to (\partial)/(\partial y)(x^2y+yz^3+z^5x) is x^2+z^3