Question

How do you use the chain rule to differentiate `y=sec^4x`?

Answer 1

`y' = 4 sec^4 x tan x`

Explanation:

You need to first realize: `y = sec^4x = (sec x)^4`

Use the Chain rule of the Power rule `(u^n)' = n u^(n-1) u'`:

Let `u = sec x`, `u' = sec x tan x`

`y' = 4(sec x)^3 (sec x tan x)`

Rearranging:
`y' = 4 sec x tan x sec^3 x`

Simplifying:
`y' = 4 sec^4 x tan x`