Question
let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 4, h'(1) = 4, g'(2) = 4, and "f '(4) = 7". find r'(1). r'(1)
Answer
112
- Find h'(x). A:h'(1) = 4.
- Find g'(x). A:g'(2) = 4.
- Find f'(x). A:f'(4) = 7.
- Apply chain rule. A:r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x).
- Evaluate r'(1). A:r'(1) = f'(g(h(1))) * g'(h(1)) * h'(1) = f'(g(2)) * g'(2) * h'(1) = f'(4) * 4 * 4 = 112.