What is (\partial)/(\partial x)(x^3-3xy) ?

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

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(\partial)/(\partial x)(x^3-3xy)

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

3 x^{2} - 3 y

Solution steps

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

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

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

= 3 x^{2} - 3 y

\frac{\partial}{\partial y} (3 x + 5 y - 1)

\frac{d}{d x} (ln (x^{2} x^{2} + 1))

\frac{d y}{d x} = \frac{( 6 x sec ( \frac{y}{x} ) + y )}{x}

cos (x) + \frac{1}{x}, \frac{π}{2}

f (x) = x^{2} + 18 x + 86, at x = 0

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