3 added 50 characters in body
source | link

EDIT

Forgot for LogPlot.

Firs of all read about tangent line. Then try to uderstand how work function getTangentVectAtValue

func[t_]:=(1-t)^(-0.5);
getTangentVectAtValue[func_,xValue_,vectLen_]:={{xValue,func[xValue]Log@func[xValue]},{xValue+vectLen,Log[(func[xValue]+(D[func[t],t]/.t->xValue)*(x-xValue))]/.x->(xValue+vectLen)}};

Show[
Plot[func[t]LogPlot[func[t], {t, 0, 1}, PlotRange -> {{0, 1}, {0.66, 20}}, 
  Frame -> {{True, True}, {True, False}}, ImageSize -> 600, 
  PlotStyle -> {Directive[Black, Thick]}, 
  BaseStyle -> {FontSize -> 30}, RotateLabel -> False, 
  AspectRatio -> 1], 
 Graphics[Arrow[getTangentVectAtValue[func, 0.8, 0.15]]]]

enter image description here

Firs of all read about tangent line. Then try to uderstand how work function getTangentVectAtValue

func[t_]:=(1-t)^(-0.5);
getTangentVectAtValue[func_,xValue_,vectLen_]:={{xValue,func[xValue]},{xValue+vectLen,(func[xValue]+(D[func[t],t]/.t->xValue)*(x-xValue))/.x->(xValue+vectLen)}};

Show[
Plot[func[t], {t, 0, 1}, PlotRange -> {{0, 1}, {0.66, 20}}, 
  Frame -> {{True, True}, {True, False}}, ImageSize -> 600, 
  PlotStyle -> {Directive[Black, Thick]}, 
  BaseStyle -> {FontSize -> 30}, RotateLabel -> False, 
  AspectRatio -> 1], 
 Graphics[Arrow[getTangentVectAtValue[func, 0.8, 0.15]]]]

enter image description here

EDIT

Forgot for LogPlot.

Firs of all read about tangent line. Then try to uderstand how work function getTangentVectAtValue

func[t_]:=(1-t)^(-0.5);
getTangentVectAtValue[func_,xValue_,vectLen_]:={{xValue,Log@func[xValue]},{xValue+vectLen,Log[(func[xValue]+(D[func[t],t]/.t->xValue)*(x-xValue))]/.x->(xValue+vectLen)}};

Show[
LogPlot[func[t], {t, 0, 1}, PlotRange -> {{0, 1}, {0.66, 20}}, 
  Frame -> {{True, True}, {True, False}}, ImageSize -> 600, 
  PlotStyle -> {Directive[Black, Thick]}, 
  BaseStyle -> {FontSize -> 30}, RotateLabel -> False, 
  AspectRatio -> 1], 
 Graphics[Arrow[getTangentVectAtValue[func, 0.8, 0.15]]]]

enter image description here

    Post Undeleted by molekyla777
2 added 377 characters in body
source | link

This is what you want?Firs of all read about tangent line. Then try to uderstand how work function getTangentVectAtValue

Show[
    LogPlot[func[t_]:=(1-\[Tau]t)^(-0.5);
getTangentVectAtValue[func_,xValue_,vectLen_]:={\[Tau]{xValue,func[xValue]},{xValue+vectLen,(func[xValue]+(D[func[t],t]/.t->xValue)*(x-xValue))/.x->(xValue+vectLen)}};

Show[
Plot[func[t], {t, 0, 1}, PlotRange -> {{0, 1}, {0.66, 20}}, 
  Frame -> {{True, True}, {True, False}}, ImageSize ->600> 600, 
  PlotStyle -> {Directive[Black, Thick]}, 
  BaseStyle -> {FontSize ->30> 30}, RotateLabel->False,AspectRatio ->1]> False, 
  AspectRatio -> Graphics[Arrow[{{01],Log[1]} 
 Graphics[Arrow[getTangentVectAtValue[func,{1 0.8,Log[20]}}]]
] 0.15]]]]

enter image description hereenter image description here

This is what you want?

Show[
    LogPlot[(1-\[Tau])^(-0.5),{\[Tau],0,1},PlotRange->{{0,1},{0.66,20}},Frame->{{True,True},{True,False}},ImageSize->600,PlotStyle->{Directive[Black,Thick]},BaseStyle->{FontSize->30},RotateLabel->False,AspectRatio->1],
    Graphics[Arrow[{{0,Log[1]},{1,Log[20]}}]]
]

enter image description here

Firs of all read about tangent line. Then try to uderstand how work function getTangentVectAtValue

func[t_]:=(1-t)^(-0.5);
getTangentVectAtValue[func_,xValue_,vectLen_]:={{xValue,func[xValue]},{xValue+vectLen,(func[xValue]+(D[func[t],t]/.t->xValue)*(x-xValue))/.x->(xValue+vectLen)}};

Show[
Plot[func[t], {t, 0, 1}, PlotRange -> {{0, 1}, {0.66, 20}}, 
  Frame -> {{True, True}, {True, False}}, ImageSize -> 600, 
  PlotStyle -> {Directive[Black, Thick]}, 
  BaseStyle -> {FontSize -> 30}, RotateLabel -> False, 
  AspectRatio -> 1], 
 Graphics[Arrow[getTangentVectAtValue[func, 0.8, 0.15]]]]

enter image description here

    Post Deleted by molekyla777
1
source | link

This is what you want?

Show[
    LogPlot[(1-\[Tau])^(-0.5),{\[Tau],0,1},PlotRange->{{0,1},{0.66,20}},Frame->{{True,True},{True,False}},ImageSize->600,PlotStyle->{Directive[Black,Thick]},BaseStyle->{FontSize->30},RotateLabel->False,AspectRatio->1],
    Graphics[Arrow[{{0,Log[1]},{1,Log[20]}}]]
]

enter image description here