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

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

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

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

3 x y^{2} + 2 x^{2} y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

y^{^{'}} = 9.8 - \frac{3 y}{3.5}

x \to \infty lim (\frac{n ^{1.5}}{ln ( n )})

x^{4} - 18 x^{2} + 81

\frac{d}{d x} (- 3 tan^{3} (sin (x)))

(6 + x) (\frac{d y}{d x}) = 9 y

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