Question

How do you find the derivative of `sin (cos (tanx) )`?

Answer 1

`-cos (cos(tan x))sin (tan x) sec^2x`

Explanation:

Use successively: If `y=f(u) and u=g(x), y'=(d/(du)f)g'.`

Here,

`(sin(cos(tan x)))'`

`cos (cos(tan x)) (cos (tan x))'`

`cos (cos(tan x)) (-sin (tan x) (tan x)'`

`cos (cos(tan x)) (-sin (tan x) sec^2x`