title: Extract and plot the first derivative of a curve in python without knowing its formula?
body: <p>I have one curve that I plot from a dataframe, I would like to extract the first derivative of the curve but I don't actually know its formula. After having the first derivative, I would like to extract the point where it reaches half of its maximum value.</p>
  <p>Is this possible to do in python?</p>
  <pre><code>
  
        X           y
  0   -0.000131   0.006983
  1   0.013764    0.006666
  2   0.028727    0.007242
  3   0.137593    0.007117
  4   0.538855    0.007305
  5   0.963937    0.008790
  6   1.318019    0.011174
  7   1.569953    0.012909
  8   1.751192    0.016706
  9   1.957168    0.020321
  10  2.125429    0.028622
  11  2.297202    0.035952
  12  2.483939    0.046041
  13  2.663194    0.056283
  14  2.855580    0.068497
  15  3.043233    0.082118
  16  3.243100    0.097764
  17  3.437318    0.111928
  18  3.639782    0.129328
  19  3.839039    0.145694
  20  4.044403    0.163474
  21  4.243966    0.182325
  22  4.453453    0.200748
  23  4.654542    0.218878
  24  4.868304    0.238715
  25  5.070615    0.254610
  26  5.288194    0.272639
  27  5.494627    0.287299
  28  5.723200    0.303031
  29  5.931618    0.315398
  30  6.189813    0.316119
  31  6.384031    0.328265
  32  6.658715    0.327107
  33  6.855071    0.333307
  34  7.138154    0.331096
  35  7.334967    0.338243
  36  7.625989    0.335927
  37  7.820513    0.343463
  38  8.077639    0.339921
  39  8.264375    0.349140
  40  8.473862    0.344021
  41  8.652201    0.349255
  42  8.816034    0.346376
  43  8.944750    0.345141
  44  9.079573    0.344968
  45  9.130418    0.344184
  46  9.255163    0.342439
  47  9.195768    0.345535
  48  9.247223    0.344030
  49  9.192867    0.345617
  50  9.281273    0.337575
  
  </code></pre>
  <p><a href="https://i.stack.imgur.com/6tyKX.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/6tyKX.png" alt="enter image description here" /></a></p>