Consider the following. \[ y=\sinh \left(4-x^{2}\right),(2,0) \] Find \( y^{\prime} \) Find the slope of the line tangent to the graph of \( y \) at the given point. Find an equation of the tangent line to the graph of the function at the given point. .

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

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.) \( \ln (3) \approx \square \)

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

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

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