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1. Solution table $$\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & f(x) & f’(x) & g(x) & g’(x) & \frac{d}{dx} \big( f(x)\cdot g(x) \big) & \frac{d}{dx} \big( \frac{f(x)}{g(x)} \big) & \frac{d}{dx} \big( \frac{g(x)}{f(x)} \big) \\ \hline 0 & 3 & –2 & –4 & 3 & (-2)\cdot 3 + 3\cdot(-4) & \dfrac{(-2)\cdot 3 - 3\cdot(-4)}{(-4)^2} & \dfrac{3\cdot 3 - (-2)\cdot(-4)}{3^2} \\ \hline 1 & 2 & –1 & 1 & 0 & (-1)\cdot 1 + 0\cdot 2 & \dfrac{(-1)\cdot 1 - 0\cdot 2}{1^2} & \dfrac{0 \cdot 2 - (-1)\cdot 1}{2^2} \\ \hline 2 & 4 & 2 & 3 & 1 & 2\cdot 3 + 1\cdot 4 & \dfrac{ 2\cdot 3 - 1\cdot 4}{3^2} & \dfrac{1\cdot 4 - 2\cdot 3}{4^2} \\ \hline \end{array}$$
1. $$(3x+7)+3(x-5) = 6x-8.$$
1. a) $$21/25.$$ b) $$x = -2, 2.$$
2. a) $$-12.$$ b) $$x = 0, 3.$$
3. $$21x^2-6x+7 , \dfrac{13}{(5t + 1)^2}$$
4. a) $$(x^3 + 3x^2)e^x.$$
5. a) $$(t+1)e^t.$$