What is (\partial)/(\partial y)(x^3-12xy+8y^3) ?

The answer to (\partial)/(\partial y)(x^3-12xy+8y^3) is 24y^2-12x

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(\partial)/(\partial y)(x^3-12xy+8y^3)

\frac{\partial}{\partial y} (x^{3} - 12 x y + 8 y^{3})

24 y^{2} - 12 x

Solution steps

\frac{\partial}{\partial y} (x^{3} - 12 x y + 8 y^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{3}) - \frac{\partial}{\partial y} (12 x y) + \frac{\partial}{\partial y} (8 y^{3})

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

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

\frac{\partial}{\partial y} (8 y^{3}) = 24 y^{2}

= 0 - 12 x + 24 y^{2}

Simplify

= 24 y^{2} - 12 x

\frac{\partial}{\partial x} (\frac{e ^{y}}{e ^{x} + e ^{y}})

\int e^{- 0.5 x^{2}} d x

\frac{\partial}{\partial x} (y + x)

\int 5^{t a n (x)} sec^{2} (x) d x

\frac{d y}{d x} = \frac{4 x + x y ^{2}}{y - x ^{2} y}

What is (\partial)/(\partial y)(x^3-12xy+8y^3) ?
The answer to (\partial)/(\partial y)(x^3-12xy+8y^3) is 24y^2-12x