is being pulled away from the wall at 2 feet per second, how fast is the top of the ladder sliding down the wall? 7) Find all open intervals on which the function \( f(x)=x^{4}-2 x^{2}+3 \) is increasing and decreasing. Then find all open intervals on which this function is concave up and concave down. 8) A divided field is to be constructed with 6000 feet of fence as shown.

\( \lim _ { m \rightarrow + \infty } m [ 2 - \sin ( n ^ { 2 } + 1 ) ] \)

\( y = ( \tan 3 x ^ { 4 } ) ^ { \sqrt { x + 3 } } \)

\( \frac{d^{4} y}{d x^{4}} \mathrm{y}=\cos 2 x \) إذا كانت

Soit \( f \) la fonction définle sur un domaine de dȩ̀inition par \( f(x)=\frac{1}{5}\left(-\sqrt{x} e^{-4 x}\right) \). On admettra que \( f \) est dérivable deux fois sur chaque intervalle contenu dans son domaine de définition. Donner la dérivée de \( f \).

Ejercicio 1. Determina la derivada de cada una de las siguientes funciones. 1. \( f(x)=10^{x} \) 2. \( f(x)=14^{x}-4^{x} \) 3. \( f(x)=9^{x}+2^{x} \) 4. \( f(x)=6^{x} \) 5. \( f f(x)=\log _{6} x \) 6. \( f(x)=\log _{15} x+3 \log _{20} x-5 \log _{2} x \) 7. \( f(x)=4 \operatorname{sen} x-5 \cos x \) 8. \( f(x)=6 \tan x-6 \csc x-3 \cos x \) 9. \( f(x)=\cos x-4 \tan x \) 10. \( f(x)=4 \sec x+5 \cot x \)