For problem 1:
We want: , but as you see, is not a function of t.
Here's how we take care of that.
Find: at . I hope that makes sense to you.
For problem 2:
We want: when .
Use the fact that:
, where to solve this.
Someone please check my computation, I caught myself making a lot of mistakes while doing this, I don't know if i caught all my mistakes.
We want , which is the rate of change of with respect to time . We will use the chain rule to obtain this. we can find by the following operation:
since derivative notations can function as fractions, the would cancel, leaving , which is what we want to find.
So let's find
Now let's find :
......by the Chain Rule
Now, when ,
So when :
So now, finally, we find :