(a) Calculate the first five derivatives of (x) x (b) Show that (n)(x) is a multiple of x n 1 2 (c) Show that (n)(x) alternates in sign as (1) n1 for n 1 (d) Find a formula for (n)(x) for n 2 Verify that the coefficient is 1 3 5 2n 3 2 n ...

a Let x x Using the Power Rule b From part a observe that The function is x 12 x 012 The first ...

(a) Calculate the first five derivatives of (x) = x. (b) Show that (n)(x) is a multiple...

Question:

(a) Calculate the first five derivatives of ƒ(x) = √x.
(b) Show that ƒ(n)(x) is a multiple of x^−n+1/2.
(c) Show that ƒ(n)(x) alternates in sign as (−1)ⁿ⁻¹for n ≥ 1.
(d) Find a formula for ƒ(n)(x) for n ≥ 2. Verify that the coefficient is ± 1 · 3 · 5 · · · 2n − 3/2ⁿ.

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