What is (\partial)/(\partial x)(x^3y+12x^2-64y) ?

The answer to (\partial)/(\partial x)(x^3y+12x^2-64y) is 3x^2y+24x

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(\partial)/(\partial x)(x^3y+12x^2-64y)

\frac{\partial}{\partial x} (x^{3} y + 12 x^{2} - 64 y)

3 x^{2} y + 24 x

Solution steps

\frac{\partial}{\partial x} (x^{3} y + 12 x^{2} - 64 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3} y) + \frac{\partial}{\partial x} (12 x^{2}) - \frac{\partial}{\partial x} (64 y)

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

\frac{\partial}{\partial x} (12 x^{2}) = 24 x

\frac{\partial}{\partial x} (64 y) = 0

= 3 y x^{2} + 24 x - 0

Simplify

= 3 x^{2} y + 24 x

What is (\partial)/(\partial x)(x^3y+12x^2-64y) ?
The answer to (\partial)/(\partial x)(x^3y+12x^2-64y) is 3x^2y+24x