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anonymous
 5 years ago
Find dy/dx by implicit differentiation.
5+3x=sin(xy)^2
anonymous
 5 years ago
Find dy/dx by implicit differentiation. 5+3x=sin(xy)^2

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0d/dx(5+3x) = d/dx(sin(xy)^2 so the left side is pretty obvious...I'm guessing its the RHS that's giving you trouble.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[d/dx \sin (xy)^2 = d/dx sinu *d/dx (u) \] if we use the chain rule and (yx)^2=u

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i got cos(xy)^2*2xy* 1*y*y' for that part but idk if its right

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so d/dx (u) is where implicit differentiation comes in. You'll have to use two rules: the product rule of differentiation (d/dt (xy) = (x)'*y + x*(y)' ) and the implicit differentiation rule.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i no how to do the product rule, its just the implicit differientiation rule that confuses me

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0rules for implicit are exactly the same for explicit; only thing is you want to keep your x' and y' til the end then factor out your y'. your x'[dx/dx] will of course equal 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so when u differenciate the y wat does that become? y*y'?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yes, y becomes y' 6y^2 becomes 12y y'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oooooooooooooooooooo!!!!

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0xy becomes: x'y + xy' not that it helps here....maybe

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmmm...I was thinking it would, since d(xy)/dx) = y+x*dy/dx?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02(sin(xy)) cos(xy) (x'y + xy') ??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so when i differenciate the whole thing it becomes 0+3=cos(xy)^2 * 2xy* (1)(y)(y')?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0u^2 Du ; u = sin(t); t = xy

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02sin(xy) cos(xy) (x'y + xy') does that help out?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yaa so thats for the right side only right

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so its a chain rule within a chain rule?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep; chain a chain lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0D(u) D(sin(t)) D(t) is what I get from it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so now i solve for y'

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, x' = 1 so we can ignore those; and solve for y'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do i divide 2sinxy*cos(xy) on both sides?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then subtract a "y" and divide it all again by "x"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so i got 3y/2sin(xy)*cos (xy)*x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats a little rough, not quite it....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03 y    x (2sin(xy)cos(xy)) x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0where did the x under the 3 come from?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets say B = (2sin(xy)cos(xy)) to clean this up... 3/B = y + xy' (3/B) y = xy' (3/B)/x  y/x = y' 3/Bx  y/x = y'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oo i turn the x into a 1

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x' = dx/dx = 1 like any good fracation does :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ooooooooo ok i see wat i did wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0omg im gonna do exactly wat u did for the test.. change that whole part to a B so i wont make a mistake

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol ..... it is easier on the eyes fer sure :)
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