Hello,Originally Posted by tttcomrader
to derivate an implicite function use:
With your problem:
Greetings and good luck with your exam!
EB
I have to find the slope of the tangent line at the point of (-2,1)
Now from my work, the derivative of this function is
Therefore the slope = 13/6
But the answer ain't right, why?
If anyone can help before I head off to the exam tomorrow morning at 9:30am I will really really really really appreicate it!!!
THANK YOU VERY MUCH!!!
earboth, he said implicit differentiation, not partial differentiation. hence it doesn't say
or anything like that
anyway ttt, your answer shows you've got some idea how to go about things but its not quite right. we have
differentiating both sides... i will write instead of to save time.
i will take you through term by term
for , that differentiates to , which i'm sure you already know.
now next i will look at
if we had
using the substitution
then
also from the we have
so
notice the dh's cancel
so differentiating implicitly with respect to x gives
which you might have also known.
where to do it quickly you are basically differentiating it with respect to y to get . then multiplying it by to give
now for the xy part you have to use the product rule
let
and
so
then
so to do it quickly when doing something with an x term times a y term you first differentiate with respect to x then multiply it by the y term... so to give you then you add that to differentiating with respect to y implicitly multiplying by the x term which gives or
so in the original problem:
this becomes
(the 15 differentiates to become 0 which you know)
so rearranging this gives
then
then you can put in x=-2, y=1
by the way i apologize with my poor attempts at explaining whats going on in these examples. i just wanted to try and explain rather than merely give answers. i would appreciate it if somebody who knows things better would come along and clear them up for me.
Thank you, that is really helpful, I think I'm ready for the exam now.
I"m heading out for it, let's hope I will come back smiling.
Again, thanks for all of your helps!
*Update*
I just got back from school, the exam is much easier than the homework, I'm pretty confidence I made an A on that.
Thank you!