What is (\partial)/(\partial y)((x+y)^3-12xy) ?

The answer to (\partial)/(\partial y)((x+y)^3-12xy) is 3(x+y)^2-12x

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(\partial)/(\partial y)((x+y)^3-12xy)

\frac{\partial}{\partial y} ((x + y)^{3} - 12 x y)

3 (x + y)^{2} - 12 x

Solution steps

\frac{\partial}{\partial y} ((x + y)^{3} - 12 x y)

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} (12 x y)

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

\frac{\partial}{\partial y} (12 x y) = 12 x

= 3 (x + y)^{2} - 12 x

\int x \cdot sin (2 x^{2}) d x

x \to 0 + lim (x^{2} e^{\frac{1}{x}})

\frac{d y}{d x} = (\frac{1 - y ^{2}}{1 - x ^{2}})^{\frac{1}{2}}

\frac{d}{d x} (2 e^{- 2 x} + \frac{1}{3} e^{x})

\frac{d}{d x} (6^{x^{2} - 3})

What is (\partial)/(\partial y)((x+y)^3-12xy) ?
The answer to (\partial)/(\partial y)((x+y)^3-12xy) is 3(x+y)^2-12x