What is (\partial)/(\partial x)(8x^3-24xy+y^3) ?

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

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(\partial)/(\partial x)(8x^3-24xy+y^3)

\frac{\partial}{\partial x} (8 x^{3} - 24 x y + y^{3})

24 x^{2} - 24 y

Solution steps

\frac{\partial}{\partial x} (8 x^{3} - 24 x y + y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x^{3}) - \frac{\partial}{\partial x} (24 x y) + \frac{\partial}{\partial x} (y^{3})

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

\frac{\partial}{\partial x} (24 x y) = 24 y

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

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

Simplify

= 24 x^{2} - 24 y

\int 8 sec^{3} (3 x) d x

y^{^{'}} + y \cdot cos (t) = sin (t) \cdot cos (t)

\int + \frac{x + 7}{x ^{2} + 4} d x

x^{3} (4 - x)

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 2

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