Chain Rule Math Example 1

Solution

1. 1
   Identify the outer function $u^4$ and the inner function $u = 3x + 1$.
2. 2
   Apply the chain rule: $\frac{d}{dx}[u^4] = 4u^3 \cdot \frac{du}{dx}$.
3. 3
   The derivative of the inner function: $\frac{du}{dx} = 3$.
4. 4
   Combine: $f'(x) = 4(3x+1)^3 \cdot 3 = 12(3x+1)^3$.