curl --request POST \
  --url https://api.iotools.cloud/v1/tool/directional-derivative-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "f": "x^2 + y^2 + z^2",
  "x": "1",
  "y": "1",
  "z": "1",
  "a": "1",
  "b": "0",
  "c": "0"
}
'

{
  "tool": "directional-derivative-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "directionalDerivative": "2",
    "gradientVector": "(2, 2, 2)",
    "maxRateOfChange": "3.4641",
    "maxRateDirection": "(0.57735, 0.57735, 0.57735)",
    "steps": "f(x, y, z) = x^2 + y^2 + z^2\n∂f/∂x = 2 * x\n∂f/∂y = 2 * y\n∂f/∂z = 2 * z\n∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)\nAt P = (1, 1, 1): ∇f(P) = (2, 2, 2)\nDirection vector v = (1, 0, 0), |v| = 1\nUnit vector u = v / |v| = (1, 0, 0)\nD_u f(P) = ∇f(P) · u = (2, 2, 2) · (1, 0, 0) = 2\nMaximum rate of change = |∇f(P)| = 3.4641, achieved along (0.57735, 0.57735, 0.57735)"
  },
  "credits_used": 5,
  "credits_remaining": null
}