Differentiation

Walkthrough

Let f(x) = x². Find f′(3).

1. 1.Recall the power rule for differentiation: d/dx(xⁿ) = n·xⁿ⁻¹.
2. 2.Identify the function: f(x) = x², so n = 2.
3. 3.Apply the power rule: f′(x) = 2·x²⁻¹ = 2x.
4. 4.Evaluate the derivative at x = 3: f′(3) = 2 × 3 = 6.
5. 5.So f′(3) = 6. This means the slope of the tangent to the curve at x = 3 is 6.