differentiate (x-2)^3 — step-by-step solution

Let's differentiate:

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

Apply the differentiation rule:

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

with f =

x - 2

ⓘ The derivative of x^n is n*x^(n-1):

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

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

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

ⓘ The derivative of a sum is the sum of the derivatives:

\frac{d}{d x} (x - 2)

1 + 0

3 \cdot (1 + 0) \cdot {(x - 2)}^{2}

ⓘ Adding 0 changes nothing:

1 + 0

1

▶Derivative:

3 \cdot {(x - 2)}^{2}