Show that if f(x) = e^{cos x} then

and find f(0) and f´(0). Differentiating the expression for f´(x), obtain f"(x) in terms of f(x) and f´(x), and find f"(0). Repeating the process, obtain f⁽ⁿ⁾(0) for n = 3, 4, 5 and 6, and hence obtain the Maclaurin polynomial of degree 6 for f(x). Confirm your answer by obtaining the series using the Maclaurin expansions of e^x and cos x.

f'(x) = f(x) sin.x