What is (\partial)/(\partial y)(xy^2+5y-6x^3+7) ?

The answer to (\partial)/(\partial y)(xy^2+5y-6x^3+7) is 2xy+5

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(\partial)/(\partial y)(xy^2+5y-6x^3+7)

\frac{\partial}{\partial y} (x y^{2} + 5 y - 6 x^{3} + 7)

2 x y + 5

Solution steps

\frac{\partial}{\partial y} (x y^{2} + 5 y - 6 x^{3} + 7)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x y^{2}) + \frac{\partial}{\partial y} (5 y) - \frac{\partial}{\partial y} (6 x^{3}) + \frac{\partial}{\partial y} (7)

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

\frac{\partial}{\partial y} (5 y) = 5

\frac{\partial}{\partial y} (6 x^{3}) = 0

\frac{\partial}{\partial y} (7) = 0

= 2 x y + 5 - 0 + 0

Simplify

= 2 x y + 5

y^{^{'}} = (x - y + 1)^{2} + (x - y)

\frac{\partial}{\partial x} (f (x) \circ g (x))

\int (\frac{8 x - 3}{12 x - 4 x ^{2} - 5}) d x

\int (6 + x + 9 e^{x}) d x

\frac{d}{d x} (arccos (\frac{12}{x}))

What is (\partial)/(\partial y)(xy^2+5y-6x^3+7) ?
The answer to (\partial)/(\partial y)(xy^2+5y-6x^3+7) is 2xy+5