[tex]y=3tanx\\\\tanx=\frac{sinx}{cosx}\Rightarrow y=\frac{3sinx}{cosx}\\\\\\y'=\frac{(3sinx)'cosx-3sinx(cosx)'}{(cosx)^2}=\frac{3cosxcosx-3sinx(-sinx)}{cos^2x}=\frac{3cos^2x+3sin^2x}{cos^2x}\\\\=\frac{3(cos^2x+sin^2x)}{cos^2x}=\frac{3(1)}{cos^2x}=\frac{3}{cos^2x}\\\\-------------------\\\\sin^2x+cos^2x=1[/tex]
