A question we had for homework was: Which of the following is equivalent to limh->0 [arcsin((3(x+h))/4) – arcsin (3x/4)]/h ?
There were multiple answer choices, but the correct answer is 3/(√16-9x^2).
The Attempt at a Solution
We've already walked through the problem in class so I know the steps to solve it, but there's one step that I didn't understand and he couldn't explain quite clearly to me. Why are we allowed to just calculate the derivative of arcsin(3x/4)? I know that according to L'Hopital's Rule we can calculate the limit by finding the limit of the derivatives, but why can we skip the other parts of the function altogether?