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Math Help - [SOLVED] differentiation of heros formula

  1. #1
    hippy chick
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    Question [SOLVED] differentiation of heros formula


    Hi all,
    i'm new to all this so bear with me if i'm asking a question that has been asked before!
    i'm in the second year of a maths and stats degree but i have to admit my calculus is terrible!!
    i need to work out an error analysis in a triangle using partial differentiation and i'm only given the length of the 3 sides.
    i know how to do the analysis but i can't figure out how to partially differentiate heros formula
    area=square root (s x (s-a)x(s-b)x(s-c)) where a,b,c are the sides of the triangle and s = (a+b+c)/2
    can anybody help?
    p.s. i know the answer because i've put it inot maple but my lecturer wants to see it done by hand!!

    thanks
    Su
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by hippy chick View Post

    Hi all,
    i'm new to all this so bear with me if i'm asking a question that has been asked before!
    i'm in the second year of a maths and stats degree but i have to admit my calculus is terrible!!
    i need to work out an error analysis in a triangle using partial differentiation and i'm only given the length of the 3 sides.
    i know how to do the analysis but i can't figure out how to partially differentiate heros formula
    area=square root (s x (s-a)x(s-b)x(s-c)) where a,b,c are the sides of the triangle and s = (a+b+c)/2
    can anybody help?
    p.s. i know the answer because i've put it inot maple but my lecturer wants to see it done by hand!!

    thanks
    Su
    At a glance, it's gonna be messy. So my questions are:

    You can't figure it out because you're intellectually stuck? Or you can't figure it out because it's a lot of work?

    One suggestion to reduce the work: To get the partial derivative wrt a, treat the area as a function of two variables, s = s(a) and a. Now use the multi-variable chain rule. Apply the same idea for partials wrt to b and c.
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