[SciPy-Dev] Return residual and derivative in gradient descent methods like Newton

Hi, Would anyone disagree or would anyone be interested in a proposal to allow the derivative to be returned from the user supplied function as an optional second argument in gradient search method like Newton? EG

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lambda x,a: (x**3-a, 3*x*"2) newton(f, x0, fprime='f2', args=(a,))

Some simple tests show that this may have a 2X speed in cases where the derivative expression requires the value of the original function call. See this issue in which I proposed this idea and wore a sample test script https://github.com/scipy/scipy/issues/8354 I proposed a way to keep the existing API and add this new feature. * If `fprime` is a callable, then same as before * If it's a string like "f2" the get fprime from second output Thanks, Mark