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**xxxq****Member**- Registered: 2006-07-04
- Posts: 2

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.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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..."

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**xxxq****Member**- Registered: 2006-07-04
- Posts: 2

I definately mean the chain rule, by multiplying du/dx and dy/du to get dy/dx,

where I think u = 1/cos(*x*)

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

The chain rule is:

f(g(x))' = f'(g(x)) * g'(x)

Which only makes sense when you are doing functions like

sin(e^x)

or

tan(cos(x))

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).

"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..."

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