Exercises

1. Calculate the differential `dy` of each of the following functions.

   `y=x^(5//2)`	`y=x^(5//2)+x^2`	`y=(x^2+3)^(5//2)`
   `y=x^(-5//2)`	`y=sqrt(x^2+3)`	`y=(ln x)^2`
   `y=x^(4//3) ln x`	`y=x(p^2+x^2)^(-1//2)`	`y=x^(-2//3) ln x`
   `y=(ln x+x)^(-1//3)`	`y=(1-sqrt(x)) ln x`	`y=(1+x^2)^(1//3)`

2. Calculate the differential `dy` of each of the following functions.

   `y=ln(x+2)`	`y=x^2+2 ln x`	`y=x^2 ln(x+2)`
   `y=ln(x^2+2)`	`y=x ln x`	`y=x ln(x^2+2)`

3. For each of the following functions, find `dy`.

   `y=ln(x^2+1)`	`y=ln(5x)`	`y=1/ln(x+5)`
   `y=2^x(x^2+1)`	`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)`