How do you differentiate tan(x) using the chain rule?
I can do it using the product rule and quotient rule, but I can't figure out how to do it with the chain rule.
Are you sure you don't mean the quotient rule?
Remeber that tan(x) = sin(x) / cos(x).
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
I definately mean the chain rule, by multiplying du/dx and dy/du to get dy/dx,
where I think u = 1/cos(x)
The chain rule is:
f(g(x))' = f'(g(x)) * g'(x)
Which only makes sense when you are doing functions like
In other words, when you have a function inside of a function. I don't think the chain rule will help you with tan(x).