Thread: [SOLVED] differentiation of heros formula

1. [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

2. Originally Posted by hippy chick

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.