What is the derivative of-4(x-4)^3 ?

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

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

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

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derivative of

- 4 (x - 4)^{3}

- 12 (x - 4)^{2}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

3 (x - 4)^{2} \frac{d}{d x} (x - 4)

= 3 (x - 4)^{2} \frac{d}{d x} (x - 4)

\frac{d}{d x} (x - 4) = 1

= - 4 \cdot 3 (x - 4)^{2} \cdot 1

Simplify

= - 12 (x - 4)^{2}

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What is the derivative of-4(x-4)^3 ?
The derivative of-4(x-4)^3 is -12(x-4)^2
What is the first derivative of-4(x-4)^3 ?
The first derivative of-4(x-4)^3 is -12(x-4)^2