clear all
; Some symbolic differentiation examples follow.

; Take the derivative of the absolute value function:
|x|
derivative

; Take the derivative of an algebraic fraction:
(2+3x)/(4+5x)
derivative

; A Taylor series demonstration:
y=x_new^n
taylor x_new 1 x_old ; build the (nth root of y) iterative approximation formula
solve verify x_new ; solve for the output variable, verifying the result
simplify ; convergent nth root approximation formula:
replace x_old x_new with x ; make x_old (input) and x_new (output) the same
x ; make sure the formula was correct by solving for x

; Another Taylor series demo:
e^x ; enter the exponential function
taylor x 10 0 ; generate a 10th order taylor series of the exponential function
laplace x ; do a Laplace transform on it
simplify ; show the structure of the result
laplace inverse x ; undo the Laplace transform
compare with 8 ; check the result
