What is (\partial)/(\partial x)(x^3-6xy+8y^3) ?

The answer to (\partial)/(\partial x)(x^3-6xy+8y^3) is 3x^2-6y

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(\partial)/(\partial x)(x^3-6xy+8y^3)

\frac{\partial}{\partial x} (x^{3} - 6 x y + 8 y^{3})

3 x^{2} - 6 y

Solution steps

\frac{\partial}{\partial x} (x^{3} - 6 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} (6 x y) + \frac{\partial}{\partial x} (8 y^{3})

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

\frac{\partial}{\partial x} (6 x y) = 6 y

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

= 3 x^{2} - 6 y + 0

Simplify

= 3 x^{2} - 6 y

n = 1 \sum \infty \frac{n ^{0}}{4 ^{n}}

x \to 7 lim (6 (7) - 2)

\frac{d}{d x} (7 x^{7} (7 - x)^{8})

x \to \infty lim ((1 + \frac{1}{7 x})^{9 x})

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

What is (\partial)/(\partial x)(x^3-6xy+8y^3) ?
The answer to (\partial)/(\partial x)(x^3-6xy+8y^3) is 3x^2-6y