Determine la derivada de la función \( f(x)=x \ln (x)-x^{3} \) Seleccione una: a. \( f^{\prime}(x)=-3 x^{2}+\ln (x)+1 \) b. \( f^{\prime}(x)=-3 x^{2}+1 \) c. \( f^{\prime}(x)=-3 x^{2}+\frac{\ln (x)}{x}-1 \) d. \( f^{\prime}(x)=-3 x^{2}+x \ln (x) \)

Determine la longitud de la curva \( x=\frac{y^{5}}{5}+\frac{1}{12 y^{3}} \) en el intervalo \( y \in[1,2] \). resultado con dos decimales.

One measure of living standards in country \( A \) is given by the following formula \( L(t)=7+4 e^{0.14 t} \) In this formula \( t \) is the number of years since 1982. Find \( L \) to the nearest hund \( \begin{array}{ll}\text { (a) } 1988 & \text { (b)1998 } \\ \text { (c)2007 }\end{array} \) \( \begin{array}{l}\text { (a) Find } L \text { for } 1988 . \\ \text { (Round to the nearest hundredth as needed.) } \\ \text { (b) Find } L \text { for } 1998 . \\ L=\square\end{array} \) (Round to the nearest hundredth as needed.) (c) Find \( L \) for 2007 .

\( \int \frac { \operatorname { cen } x d x } { \cos x ( \cos x - 1 ) } \)

Ercontrar \( f(t) \) si \( F(s)=\frac{5}{s^{2}+4}+\frac{20 s}{s^{2}+9} \)

Find the value. \[ \begin{array}{l}\operatorname{In}\left(\frac{92}{20}\right) \\ \text { In }\left(\frac{92}{20}\right) \approx \square \\ \text { (Round the final answer to four decimal places as needed. Round }\end{array} \]