Combine rules to differentiate the following functions. (a) f(x)=7xex By the product rule, f'(x) = 7x (2ex)

Combine rules to differentiate the following functions.

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(a) f(x)=7xex By the product rule, f'(x) = 7x (2ex) + ex (7) = 14xe2x+7e2x =7e2x (2x+1) (c) y = (e-4x)3 By the generalized power function rule, (b) y = 2x45x y' = 2x4 (5e5x)+ex (8x) = 10x45x+8x35x = 2x35x (5x+4) y' = 3. (e-4x)2. (-4e-4x) =-12(e-4x)3-12e- -12x Note: By the properties of exponents, (e-4x)3 = e12x and the derivative of e-12x is, of course, simply -12e-12x (d) f(x)=(ex + e-3x) 5 f'(x)=5. (ex +e-3x) 4. (4e4x-3e-3x) =(20e4x-15e3x) (e 4x + e 3x) 4