About NUR ARINA BASILAH BINTI KAMISAN Expertise i can answer derivatives and integral questions but not so expert in answering limits,vector and infinite series.
Experience i teached calculus for foundation students at university malaya and i also teached tutorial class in university for subject differential equation when i was doing my degree.currently i'm teaching algebra for foundation students.
Education/Credentials i have degree in mathematics with education and now i'm futhering my study in master of statistics at university malaya.
Expert: NUR ARINA BASILAH BINTI KAMISAN - 7/21/2008
Question "QUESTION: I had asked this question originally on the site:www.thestudentroom.co.uk But,I couldnot understand the answer as they said to apply chain rule of differentiation.Since the question is not like the general question on which we apply chain rule,I couldnot understand it.The attached picture on this question can be found on this link:http://www.thestudentroom.co.uk/attachment.php?attachmentid=56069&d=1216384477
The question goes like this-
In triangle PQR,
(chord PQ)^2=(PR)^2+(QR)^2=(delta x)^2+(delta y)^2
But,
how come this
(chord PQ/delta s(arc AP))^2*(delta s/delta x)^2=1+(delta y/delta x)^2
Please help me through this since I am facing lots of problem on this.
i could not open the link on the studentroom website because they asked for log on id and i don't have one.so here is the answer.
you have a triangle.just imagine the triangle PQR ok.because PQR is a right angle triangle,we can apply the theorem pythagoras.(for more info about theorem pythagoras,u can visit this website http://en.wikipedia.org/wiki/Pythagorean_Theorem)
from theorem pythagoras the hypotenuse will be the chord PQ and the other two side will be QR and PR.so,when we substitute in the theorem we will get:
(chord PQ)^2=(PR)^2 + (QR)^2 which was also equal to
=(delta x)^2 + (delta y)^2
now,chain rule is something like this:
dy/dx=(dy/du) x (du/dx)
u can cancel out the du and will get dy/dx (try to write it back in a paper.so u can see it more clear).now back to your question,you have an equation like this:
(chord PQ/delta s (arc AP))^2*(delta s/delta x)^2
=(chord PQ)^2/(delta s(arcAP))^2 * (delta s)^2/(delta x)^2
(note that delta s(arc AP)=delta s)
=(chord PQ)^2/(delta s)^2 * (delta s)^2/(delta x)^2 -->(here where we apply the chain rule,we can cancel out the delta s^2)
=(chord PQ)^2/(delta x)^2
and because (chord PQ)^2=(delta x)^2 + (delta y)^2,substitute it for (chord PQ)^2 in the equation above and u will have:
=[(delta x)^2 + (delta y)^2]/(delta x)^2
= (delta x)^2/(delta x)^2 + (delta y)^2/(delta x)^2
= 1 + (delta y)^2/(delta x)^2
= 1 + (delta y/delta x)^2 #proved
-->try to write it back in a paper and you can understand it
