Question

Find the first three derivatives of f(x)=tan3x.

Answer 1

To help you get started: look up the derivative of the tangent function. What is the derivative of the simpler function y = tan x?
Now return to y = tan 3x. Since the argument (3x) is now a function in its own right, we need to apply the Chain Rule: Find the derivative of y = tan (3x) with respect to (3x). Then, multiply this by the derivative of the (separate) function (3x).
Try this, please.

Answer 2

Well I get the first derivative which is,
3sec^2(3x)

Answer 3

I don't get how to do the second derivative.

Answer 4

second derivative \[\frac{ 18\tan 3x }{ \cos ^{2}3x}\]

Answer 5

Think of y' as y' = 3*(sec(3x))^2. This is a POWER FUNCTION. Apply the constant multiplier rule, the power rule and the chain rule, in that order, to determine the derivative of 3*(sec(3x))^2; the result will be y''.

Answer 6

If ceyhun is correct, then y''' is found using the QUOTIENT rule (and several others).

Answer 7

Well the answer in the book comes out to be,
18sec^2(3x)tan(3x)

Answer 8

What's more important is how we arrive at that answer. Please consider how you'd do this using the basic rules of differentiation. Given the practice problem y = tan x / cos x, how would you find the derivative?

Answer 9

Answer: the derivative of y = (tan x)/(cos x), following the quotient rule, is

dy (cos x)*(sec x)^2 - (tan x)*(-sin x)
-- = -----------------------------
dx (cos x)^2

If this is unclear, please ask questions, and then I (or someone else) will help you complete the work necessary to solve this homework problem.