1. ## differentiating implicitly....little help

i understand the main concept of differentiating implicitly, however i cant seem to get this problem,

sin(xy)=6x+7

mathaction

2. Originally Posted by mathaction
i understand the main concept of differentiating implicitly, however i cant seem to get this problem,

sin(xy)=6x+7

mathaction
you need the chain rule (coupled with the product rule) for the LHS. here goes:

$\sin (xy) = 6x + 7$

differentiating implicitly with respect to x, we get:

$\cos (xy) \cdot (y + x~y') = 6$

now solve for $y'$

3. Originally Posted by Jhevon
you need the chain rule (coupled with the product rule) for the LHS. here goes:

$\sin (xy) = 6x + 7$

differentiating implicitly with respect to x, we get:

$\cos (xy) \cdot (y + x~y') = 6$

now solve for $y'$
yeah when i was doing it for some reason i was putting dy/dx on the cos(xy), but this helped, i came up with...

(6-ycos(xy))/(xcos(xy))

4. Originally Posted by mathaction
yeah when i was doing it for some reason i was putting dy/dx on the cos(xy), but this helped, i came up with...

(6-ycos(xy))/(xcos(xy))
that's correct

5. i have just one more, about implicity differentiation...for this problem...

x^3 + 5x^2y + 2y^2 = 4y + 11

the last answer i came up with was...

(-3x^2-10xy)/(5x^2+4y-1)

then it wanted the slope of the tangent line at (1,2), but when i plugged these in the answer was wrong, and im sure thats from a faulty differentiation, can you please let me know where i messed up...thanks

6. Originally Posted by mathaction
i have just one more, about implicity differentiation...for this problem...

x^3 + 5x^2y + 2y^2 = 4y + 11

the last answer i came up with was...

(-3x^2-10xy)/(5x^2+4y-1)

then it wanted the slope of the tangent line at (1,2), but when i plugged these in the answer was wrong, and im sure thats from a faulty differentiation, can you please let me know where i messed up...thanks
the 1 should be a 4. it comes from the derivative of 4y

7. Originally Posted by Jhevon
the 1 should be a 4. it comes from the derivative of 4y
ok, so then the rest of it is good then...

8. Originally Posted by mathaction
ok, so then the rest of it is good then...
yes. change that 1 to a 4 and you should be fine

9. Originally Posted by Jhevon
yes. change that 1 to a 4 and you should be fine
yeah i had it that way before, and just didnt do the basic algebra right, just gotta be careful for the really easy stuff to overlook...thanks alot