What is the derivative of-4x^3 ?

The derivative of-4x^3 is -12x^2

What is the first derivative of-4x^3 ?

The first derivative of-4x^3 is -12x^2

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\frac{d}{d x} (- 4 x^{3})

- 12 x^{2}

Solution steps

\frac{d}{d x} (- 4 x^{3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 4 \frac{d}{d x} (x^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 4 \cdot 3 x^{3 - 1}

Simplify

= - 12 x^{2}

x \frac{d y}{d x} + y = 9 x y^{2}, y (1) = 2

x \to 4 - lim (\frac{2 x}{x - 4})

f (x) = \frac{7 x}{x - 1}, (2, 14)

\frac{\partial}{\partial x} (sin (8 x) cos (4 y))

\int_{0}^{1} x (\frac{2 ( x + 1 )}{3}) d x