Exercises

1. Calculate the derivative of each of the following functions.

   `lntext[(]x+2text[)]`	`x^2+2 ln x`	`x^2 lntext[(]x+2text[)]`
   `lntext[(]x^2+2text[)]`	`x ln x`	`x lntext[(]x^2+2text[)]`

2. For each of the following functions, find `(dy)/(dx)`.

   `y=lntext[(]x^2+1text[)]`	`y=ln 5x`	`y=1/(lntext[(]x+5text[)])`
   `y=2^xtext[(]x^2+1text[)]`	`y=e^(ln 5x)`	`y=1/(x^2+5)`
   `y=e^(x^2)`	`y=1/(x+5)`	`y=1/sqrt(x^2+5)`
   `y=sqrt(x^3+1)`	`y=1/sqrt(x+5)`	`y=1/ln(x^2+5)`

3. Find the slope of the tangent line to the curve `x^3+y^3=28` at `text[(]1,3text[)]`.
4. Find the slope of the tangent line to the curve `x^2-y^2=5` at `text[(]3,2text[)]`.
5. Find (approximately) a number `x` that solves the equation `x=5 ln x`.