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@@ -6,8 +6,7 @@
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(:use #:cl)
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(:export :derive
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:csc
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- :sec
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- :cot))
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+ :sec))
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(in-package #:derive)
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@@ -19,7 +18,7 @@ Derives an equation using the normal rules of differentiation."
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(declare (cons equation))
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(let ((op (first equation)))
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(cond
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- ((member op '(sin cos tan csc sec cot sqrt))
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+ ((member op '(sin cos tan csc sec cot))
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(chain equation))
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((equal op 'expt)
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(power (rest equation)))
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@@ -75,7 +74,21 @@ Derive using quotient rule"
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"chain -- (chain equation)
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Apply the chain rule to the equation"
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(declare (cons equation))
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- )
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+ (let ((op (first equation))
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+ (arg (second equation)))
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+ (case op
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+ (sin
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+ `(* (cos ,arg) ,(derive arg)))
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+ (cos
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+ `(* (- (sin ,arg)) ,(derive arg)))
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+ (tan
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+ `(* (expt (sec ,arg) 2) ,(derive arg)))
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+ (csc
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+ `(* (- (csc ,arg)) (cot ,arg) ,(derive arg)))
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+ (sec
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+ `(* (sec ,arg) (tan ,arg) ,(derive arg)))
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+ (cot
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+ `(* (- (expt (csc ,arg) 2)) ,(derive arg))))))
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(defun power (eq)
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"power -- (power rest)
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@@ -97,9 +110,4 @@ Calculate the cosecant of x"
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Calculate the secant of x"
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(/ (cos x)))
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-(defun cot (x)
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- "cot -- (cot x)
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-Calculate the cotangent of x"
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- (/ (tan x)))
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-
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;;; End derive
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