Esta regla establece: tomando el denominador \( g(x) \) multiplicado por la derivada del numerador \( f(x) \) restado al numerador \( f(x) \) multiplicado por la derivada del denominado \( g(x) \), todo dividido por el cuadrado del denominador \( g(x) \) a. Derivada de una suma de funciones b. Derivada de un producto de funciones c. Derivada de un cociente de funciones d. Derivada de un función seno

Use a Riemann sum to approximate the area under the graph of \( f(x)=4 e^{-x} \) on the interval \( 0 \leq x \leq 1 \) using \( n=5 \) subintervals with the selected points as the right end points. The area is approximately \( \square \) units. (Round to six decimal places as needed.)

7. c) \( \frac{1}{1+x}-\frac{2}{x^{2}-1} \)

2. \( y=\frac{3^{\sqrt{x}}}{\lg (3-x)} \)

A national fast food company has just analyzed the effect of the latest sales promotion. It has determined that the sales decay for its milkshakes is given by \( S=285,000 e^{-0.7 x} \), where \( S \) is the weekly sales and \( x \) is the number of weeks that have passes since the end of the sales promotion. a) Determine the sales 2 weeks after the end of the promotion: Round answer to 2 decimal places. Sales \( =\$ \) b) If no new campaign is started, how many weeks after the end of the promotion will sales drop below 30,000 ? Round answer to 1 decimal place. Num. weeks =

\( : \int _ { - 3 } ( x ^ { 2 } + 7 x - 8 ) d x \)