softmax function implementation in js

softmax.js

// Fork & examples for the one-line version by @vladimir-ivanov:
//let softmax = (arr) => (index) => Math.exp(arr[index]) / arr.map(y => Math.exp(y)).reduce((a, b) => a + b);
//
// Also see comments for improvements

function softmax(arr) {
    return arr.map(function(value,index) { 
      return Math.exp(value) / arr.map( function(y /*value*/){ return Math.exp(y) } ).reduce( function(a,b){ return a+b })
    })
}

example1=[ 0.9780449271202087,
  0.01590355671942234,
  0.0019390975357964635,
  0.0015482910675927997,
  0.0012942816829308867,
  0.0006004497990943491,
  0.0004827099328394979,
  0.0001868270628619939 ]
softmax1=softmax(example1)

example2= [ 
  { prob: 0.32289665937423706, cat: '25_32' },
  { prob: 0.15404804050922394, cat: '38_43' },
  { prob: 0.03673655539751053, cat: '4_6' },
  { prob: 0.01545996405184269, cat: '48_53' },
  { prob: 0.011709162034094334, cat: '15_20' },
  { prob: 0.008010754361748695, cat: '8_13' },
  { last: true, prob: 0.0054732030257582664, cat: '60+' } ].map(function(v){return v.prob})
softmax2=softmax(example2)

example3=[ { prob: 0.125, cat: '25_32' },
  { prob: 0.125, cat: '38_43' },
  { prob: 0.125, cat: '15_20' },
  { prob: 0.125, cat: '8_13' },
  { prob: 0.125, cat: '4_6' },
  { prob: 0.125, cat: '48_53' },
  { prob: 0.125, cat: '60+' },
  { prob: 0.125, cat: '0_2' } ].map(function(v){return v.prob})
softmax3=softmax(example3)

By any chance, does anyone have an example of the softmax derivative ? Or is able to tell me if this one is correct:

function derivative(arr) {
  const values = softmax(arr);

  return arr.map((x, i) => {
    return values[i] * (values[i] - (i === 0 ? 1 : 0));
  });
}