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

The answer to (\partial)/(\partial y)(3x^2y+5xy^3) is 3x^2+15xy^2

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

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

3 x^{2} + 15 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (5 x y^{3}) = 15 x y^{2}

= 3 x^{2} + 15 x y^{2}

\frac{( 3 - x )}{4 x}

\int cos^{4} (3 - x) sin (3 - x) d x

y = x, y = 1 - x^{2}, - 1, 2

- \frac{39}{( 8 x + 5 ) ^{2}}, at x = 2

\int_{0}^{4} \frac{12}{x ^{2} + 5 x + 6} d x

What is (\partial)/(\partial y)(3x^2y+5xy^3) ?
The answer to (\partial)/(\partial y)(3x^2y+5xy^3) is 3x^2+15xy^2