Use the quotient rule to take the derivative of the following functions: \( \begin{array}{ll}\text { 1. } y=\frac{x^{2}-4 x}{2 x+6} & \text { 2. } x+x y+y=2 \\ \text { 3. } y=x^{2} y+1 & \text { 4. } f(x)=\frac{\sqrt{x-1}}{\sqrt{3-x}}\end{array} \)

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 \( f \).

Find the Maclaurin series for the following function and determine its radius of convergence \( R \). \( f(x)=\ln \left(\frac{1+x}{1-x}\right) \). \( R=\square \) Use the first four terms of the series to approximate \( \ln (3) \). (Round your answer to six decimal places.) \( \ln (3) \approx \square \)

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

8. \( \int \frac{8 x^{2} d x}{\left(x^{3}+2\right)^{3}} \)

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. \( f(x)=4 \sec x+5 \cot x \)