Suppose f is differentiable on R and α is a real number. Let F(x) = f(x^α) and G(x) = [f(x)]^α. Find expressions for (a) F’(x) and (b) G’(x)?

👨🏻‍🏫 學術台數學

[匿名]

2017-02-15 6:08 am

回答 (1)

cidyah

2017-02-15 6:55 am

α)
F(x) = f(x^α)
F'(x) = f'(x^α) d/dx (x^α)
F'(x) = f'(x^α) (α) x^(α-1)
F'(x) = α x^(α-1) f'(x^α)

b)
G(x) = (f(x))^α
G'(x) = α (f(x))^(α-1) f'(x)

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