What is (\partial)/(\partial x)(x^3-12x+y^3-27y) ?

The answer to (\partial)/(\partial x)(x^3-12x+y^3-27y) is 3x^2-12

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(\partial)/(\partial x)(x^3-12x+y^3-27y)

\frac{\partial}{\partial x} (x^{3} - 12 x + y^{3} - 27 y)

3 x^{2} - 12

Solution steps

\frac{\partial}{\partial x} (x^{3} - 12 x + y^{3} - 27 y)

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) + \frac{\partial}{\partial x} (y^{3}) - \frac{\partial}{\partial x} (27 y)

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

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

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

\frac{\partial}{\partial x} (27 y) = 0

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

Simplify

= 3 x^{2} - 12

What is (\partial)/(\partial x)(x^3-12x+y^3-27y) ?
The answer to (\partial)/(\partial x)(x^3-12x+y^3-27y) is 3x^2-12