What is (\partial)/(\partial y)(x^2y^4+z^3) ?

The answer to (\partial)/(\partial y)(x^2y^4+z^3) is 4x^2y^3

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(\partial)/(\partial y)(x^2y^4+z^3)

\frac{\partial}{\partial y} (x^{2} y^{4} + z^{3})

4 x^{2} y^{3}

Solution steps

\frac{\partial}{\partial y} (x^{2} y^{4} + z^{3})

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{2} y^{4}) + \frac{\partial}{\partial y} (z^{3})

\frac{\partial}{\partial y} (x^{2} y^{4}) = 4 x^{2} y^{3}

\frac{\partial}{\partial y} (z^{3}) = 0

= 4 x^{2} y^{3} + 0

Simplify

= 4 x^{2} y^{3}

\int \frac{x ^{2} - 289}{x} d x

x \to 7 lim (18)

\int ln (\frac{x}{x + 1}) d x

\int_{0}^{4} x^{2} - 4 x + 3 d x

\frac{d}{d x} (d - b - a x - \frac{d}{x ^{2}})

What is (\partial)/(\partial y)(x^2y^4+z^3) ?
The answer to (\partial)/(\partial y)(x^2y^4+z^3) is 4x^2y^3