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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{\partial}{\partial y} (4 x) = 0

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

Simplify

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

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0, y^{^{'}} (0) = 7

y = x^{3} - 2 x + 2 (2.6)

\frac{d}{d x} (x + \frac{2}{sin ( x )})

\int_{0}^{\frac{π}{2}} 24 x^{2} sin (x) d x

x \to 0 - lim (\frac{3}{x ^{2} - x})

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