Question

Please open the image and help me

Answer 1

3.

`y=\sec^3x+\cot^2(2x)`

Use the chain rule:

`y'=(\sec^3x)'+(\cot^2(2x))'`

`y'=3\sec^2x(\sec x)'+2\cot(2x)(\cot(2x))'`

`y'=3\sec^2x(\sec x\tan x)-2\cot(2x)\csc^2(2x)(2x)'`

`y'=3\sec^3x\tan x-4\cot(2x)\csc^2(2x)`

4.

`y=\sin(cos(3x))`

Same as before:

`y'=(\sin(\cos(3x)))'`

`y'=\cos(\cos(3x))(\cos(3x))'`

`y'=-\cos(\cos(3x))\sin(3x)(3x)'`

`y'=-3\cos(\cos(3x))\sin(3x)`