3.
[tex]y=\sec^3x+\cot^2(2x)[/tex]
Use the chain rule:
[tex]y'=(\sec^3x)'+(\cot^2(2x))'[/tex]
[tex]y'=3\sec^2x(\sec x)'+2\cot(2x)(\cot(2x))'[/tex]
[tex]y'=3\sec^2x(\sec x\tan x)-2\cot(2x)\csc^2(2x)(2x)'[/tex]
[tex]y'=3\sec^3x\tan x-4\cot(2x)\csc^2(2x)[/tex]
4.
[tex]y=\sin(cos(3x))[/tex]
Same as before:
[tex]y'=(\sin(\cos(3x)))'[/tex]
[tex]y'=\cos(\cos(3x))(\cos(3x))'[/tex]
[tex]y'=-\cos(\cos(3x))\sin(3x)(3x)'[/tex]
[tex]y'=-3\cos(\cos(3x))\sin(3x)[/tex]
