DIFFERENTIATION

creator:  Peter Knipp
repo:  github.com/pknipp/calculus

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integration
root-finding
max-finding
1st order differential equations
2nd order differential equations

In the url bar after https://basic-calculus.herokuapp.com/differentiation type the following:

/<value of x at which to calculate function and derivatives>/<function of x>

The function may be any algebraically legal combination of the variable letter(s), numbers, parentheses, and/or binary operations +, -, *, ** (encouraged) or ^ (discouraged), PI and/or the most common unary functions: abs, acos, acosh, acot, acoth, acsc, acsch, asec, asech, asin, asinh, atan, atanh, cbrt, ceil, cos, cot, csc, exp, exp2, exp_m1, floor, fract, ln, ln_1p, log10, log2, sec, signum, sin, sqrt, tan, and trunc. (See docs for more information.) To represent division you must use either div, d, DIV or D because the usual division symbol (/) has special meaning in a url. Implied multiplication is allowed. Spaces are allowed but discouraged.
The construction rules for the values of any variable in the url are the same as those for the function except - of course - it cannot include the letter which represents the variable.
example:To differentiate the function 2x + 3/(x⁴ + 5) at x = 1, type /1/2x+3d(x**4+5) after the current url address. The results for the values of the function and of its first three derivatives should be 2.5, 1.66..., -0.55..., and 1.11...
algorithms: finite differences for small values of Δx, excluding any reference to the particular point itself in the case of a removable singularity
json: Type '/api' in the url bar immediately before 'differentiation' if you would like the result in json rather than in html. A successful response will contain three properties: 'x' (a float), 'nonsingular' (a boolean reflecting whether or not the function has a removable singularity), and 'derivs' (a 4-element array of floats whose values represent the function value and first through third derivatives, respectively). An unsuccessful response will have one property: 'message' (a string reporting the error).