hw11 differentiation rules ii (target c1, c2, c5; §3.3)\nscore: 0/8 answered: 0/8\nquestion 1\n(1) which is…

Explanation:

Step1: Recall product - rule formula

The product - rule for the derivative of the product of two functions (f(x)) and (g(x)) is ((fg)'=fg'+gf').

Step2: Identify functions for (f(x)=x^{4}e^{x})

Let (u = x^{4}) and (v=e^{x}). Then (u'=\frac{d}{dx}(x^{4}) = 4x^{3}) and (v'=\frac{d}{dx}(e^{x})=e^{x}).

Step3: Apply product - rule

Using the product - rule ((uv)'=uv'+vu'), we substitute (u = x^{4}), (u' = 4x^{3}), (v = e^{x}), and (v'=e^{x}). So (f'(x)=x^{4}e^{x}+4x^{3}e^{x}=x^{3}e^{x}(x + 4)).

Answer:

(1) ((fg)'=fg'+gf') (2) (x^{3}e^{x}(x + 4))