Question

find the derivative of tan^9 x

Answer 1

Show me your best guess and I'll show you exactly where you need to correct yourself. Break the problem up if that's how you learned it, try to show the most you can so I can help you see where to fix yourself. =)

Answer 2

Just take a guess @jschroeck92 . You've got nothing to lose, I won't help you until you give something in return lol.

Answer 3

im thinking it's sec^18 x because the derivative of tanx is sec^2 x but im not sure

Answer 4

You can apply here power rule. First you let x = tan x
Hence, your given will now be x^9, right?
Then, do the power rule. It will then be,
9x^8 dx, right?
Hence
9tan^8 (x) (*times derivative of tanx)
Now what will be the final answer? Did you get what I mean?

Answer 5

kind of, but what about the fact that it is a trig function? They have special rules that need to be applied

Answer 6

the special rule will enter in the (dx)
that's why our representation is 9x^8 (dx)
dx represents the dervative of any function x, and in this case, it is a tanx --> so just input its derivative. and you'll have the answer.

Answer 7

So here it might be easier to think of this as two separate functions to apply the chain rule.

So if we call tan(x)=f(x) then we have:

[f(x)]^9

So we can take the derivative of the outside and multiply it times the derivative of the inside like this:

9[f(x)]^8 * f'(x)

and then you can take the derivative of f(x)=tanx to find the outside part as well.

Answer 8

okay, thanks