Partial Derivatives and the Gradient
~12 mincode completion
Implement gradient_at(x, y) returning as a two-element list, using the analytic formulas above.
Examples
At (2, 1) the partials are 4 and 7
- Input
- gradient_at(2, 1)
- Output
- [4, 7]
On the y axis the x partial vanishes but the y partial does not
- Input
- gradient_at(0, 2)
- Output
- [0, 12]
At the origin the surface is flat to first order
- Input
- gradient_at(0, 0)
- Output
- [0, 0]
Hints
Hint 1
Work directly with the arguments x, y and return the result rather than printing it.
Hint 2
Watch for this: treats the frozen variable as if it were zero.
Requirements
x: first coordinatey: second coordinateReturn list of two floats: [df/dx, df/dy]
Constraints
Standard library only, no imports required
Time limit: 200 ms, Memory: 64 MB
Try similar problems(4)
Where this shows up
~12 min
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Python
def gradient_at(x, y):
"""
Analytic gradient of f(x, y) = x^2*y + y^3.
Args:
x: first coordinate
y: second coordinate
Returns:
list of two floats: [df/dx, df/dy]
"""
# YOUR CODE HERE
pass