What is (\partial)/(\partial x)(x^2y+y^3-27y) ?

The answer to (\partial)/(\partial x)(x^2y+y^3-27y) is 2xy

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(\partial)/(\partial x)(x^2y+y^3-27y)

\frac{\partial}{\partial x} (x^{2} y + y^{3} - 27 y)

2 x y

Solution steps

\frac{\partial}{\partial x} (x^{2} y + y^{3} - 27 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (y^{3}) - \frac{\partial}{\partial x} (27 y)

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

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

\frac{\partial}{\partial x} (27 y) = 0

= 2 y x + 0 - 0

Simplify

= 2 x y

\int (1 + x^{2} + \frac{1}{1 + x ^{2}}) d x

x \to 2 lim (x^{2} + 3 x + 4)

\int e^{- a x} d x

\frac{d y}{d x} = \frac{8}{7} y

y^{^{''}} + 144 y = sec (12 x)

What is (\partial)/(\partial x)(x^2y+y^3-27y) ?
The answer to (\partial)/(\partial x)(x^2y+y^3-27y) is 2xy