Partial Derivatives in LISP
So my old friend and archnemisis is building a calculator, but with LISP (more specifically, the SCHEME dialect). He has come to a problem with partial derivatives, and I must admit it is a devil of a problem.
He programmed a derivative to return several things conditionally
Thus one has to enter the function (lambda (x) (f)) and has returned several things (he plans to tackle integrals the same way).
(define (deriv (lambda (x) (f)) dx)
(cond (= f (^ x n)) (* n (^ f (- n 1)))
(= f (ln (abs x))) (^ x -1)
(= f (sin x)) (cos x)
(= f (cos x)) (* (sin x) (-1))
(= f (tan x)) ((^ sec 2) x)
(= f (csc x)) (* (* (-1) (csc x)) (cot x))
(= f (sec x)) (* (sec x) (tan x))
(= f (cot x)) (* ((^ csc 2) x) (-1))
(= f (exp x)) (exp x)
(= f (^ a x)) (* (ln a) (^ a x))))
I can't figure out for the life of me how to help him make a partial derivative without creating errors!