Differentiate the following natural exponential functions, using the rule found in (11.5): d/dx[es(x)] = e8(x). g'(x). (a)

Differentiate the following natural exponential functions, using the rule found in (11.5):

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d/dx[es(x)] = e8(x). g'(x). (a) f(x) = ex Let g(x)=6x, then g'(x) = 6, and from (11.5), f'(x) = ex. 6 = 6e6x (c) f(x)=e3x f'(x) = e3x-6x = 6xe3x (e) y = 5e7-x y' = 5e7-x-3x =-15x27-x (b) y = e8x Let g(x)=-8x, then g'(x)=-8, and from (11.5), y' = e8x-8 =-8e-8x (d) y=4x-9 y' =4x-9.4 (f) y = y' = = 4e4x-9 (1/2)x4 (1/2)x (4x) . = {xe(1/2)x4