documentclass[pstricks]{standalone}
usepackage{pstricks,pst-plot,pstricks-add}

begin{document}
defF{x RadtoDeg dup dup cos exch 2 mul cos add exch 3 mul cos add}
defFp{x RadtoDeg dup dup sin exch 2 mul sin 2 mul add exch 3 mul sin 3 mul add neg}
psset{plotpoints=1001}
begin{pspicture}(-7.5,-2.5)(7.5,4)%Xpsgrid
psaxes{->}(0,0)(-7.5,-2)(7.5,3.5)
psplot[linewidth=3pslinewidth]{-7}{7}{F}
psset{linecolor=red, arrows=<->, arrowscale=2}
multido{n=-7+1}{8}{psplotTangent{n}{1}{F}}
psset{linecolor=magenta, arrows=<->, arrowscale=2}%
multido{n=0+1}{8}{psplotTangent[linecolor=blue, Derive=Fp]{n}{1}{F}}
end{pspicture}

end{document}

documentclass[pstricks,border=0bp,12pt,dvipsnames]{standalone}
usepackage{pstricks-add}

usepackage[nomessages]{fp}

FPsetTrigLabelBase{4}
FPevalXMin{0-pi}
FPevalXMax{2*pi}
FPsetYMin{-3}
FPsetYMax{3}

FPevalDeltaX{pi/TrigLabelBase}
FPevalDeltaY{1}

FPevalLeft{XMin-DeltaX/2}
FPevalRight{XMax+DeltaX/2}
FPevalBottom{YMin-DeltaY/4}
FPevalTop{YMax+DeltaY/4}

newlengthWidthWidth=12cm
newlengthHeightHeight=6cm

newlengthurxurx=15pt
newlengthuryury=15pt
newlengthllxllx=-5pt
newlengthllylly=-5pt



psset
{
    algebraic,
    urx=urx,
    ury=ury,
    llx=llx,
    lly=lly,
    plotpoints=1000,
    trigLabels,
    trigLabelBase=TrigLabelBase,
    xAxisLabel=$x$,
    yAxisLabel=$y$,
    tickcolor=gray,
    ticksize=0 -4pt,
    labelFontSize=scriptstyle,
}



deff{cos(x)+cos(2*x)/2+cos(3*x)/3}
deffp{Derive(1,f)}



begin{document}

begin{psgraph}[dx=DeltaX,dy=DeltaY,linecolor=gray]{->}(0,0)(Left,Bottom)(Right,Top){dimexprWidth-urx+llx}{!}%{dimexprHeight-ury+lly}
    psplot[linecolor=NavyBlue]{XMin}{XMax}{f}
    pstVerb{/xxx {Pi 4 div} def}%
    psset{arrows=<->}
    psplotTangent[linecolor=ForestGreen]{xxx}{3}{f}% tangent line
    psplotTangent[linecolor=Maroon,Derive={-1/fp}]{xxx}{3}{f}% normal line
end{psgraph}

end{document}