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

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

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

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

3 x^{2} - 12 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (8 y^{3}) = 0

= 3 x^{2} - 12 y + 0

Simplify

= 3 x^{2} - 12 y

(x^{2} - 5 x + 1)^{4}

\int_{1}^{3} (2 x^{2} - 12 x + 13) d x

\int (\frac{ln ( x )}{x})^{2} d x

(ln (x + 2))^{^{'}}

x \to 7 - lim (\frac{6 x}{x - 7})

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