Find derivative of f(x)= arctan(e^4x)

i know the formula is 1/ (1+x^2), x being the stuff inside tan, but i can't seem to do it right : (

Ataxi cab charges $1.75 for the flat fee and $0.25 for each time. write an in equality to determine how many miles eddie can travel if he has $15 to spend.

Find the length of the following tangent segments to the circles centered at o and o' whose radii are 5 and 3 respectively and the distance between o and o' is 12. what is the tangent segment of cd?

The ratio pv to nrt is plotted against pressure for ch4 at 0°c and 200°c. why does the curve for 0°c drop below the horizontal line for an ideal gas whereas the curve for 200°c does not?