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d/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.
\[d/dx \sin (xy)^2 = d/dx sinu *d/dx (u) \] if we use the chain rule and (yx)^2=u
i got cos(xy)^2*2xy* 1*y*y' for that part but idk if its right
so 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.
i no how to do the product rule, its just the implicit differientiation rule that confuses me
rules 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
so when u differenciate the y wat does that become? y*y'?
yes, y becomes y' 6y^2 becomes 12y y'
xy becomes: x'y + xy' not that it helps here....maybe
...but it might lol
hmmm...I was thinking it would, since d(xy)/dx) = y+x*dy/dx?
2(sin(xy)) cos(xy) (x'y + xy') ??
so when i differenciate the whole thing it becomes 0+3=cos(xy)^2 * 2xy* (1)(y)(y')?
u^2 Du ; u = sin(t); t = xy
2sin(xy) cos(xy) (x'y + xy') does that help out?
yaa so thats for the right side only right
so its a chain rule within a chain rule?
yep; chain a chain lol
D(u) D(sin(t)) D(t) is what I get from it
ooooooo ok i get it!
so now i solve for y'
yep, x' = 1 so we can ignore those; and solve for y'
do i divide 2sinxy*cos(xy) on both sides?
its a good start :)
then subtract a "y" and divide it all again by "x"
so i got 3-y/2sin(xy)*cos (xy)*x
is that correct?
thats a little rough, not quite it....
wat did i do wrong?
3 y ---------------- - -- x (2sin(xy)cos(xy)) x
where did the x under the 3 come from?
lets 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'
oo i turn the x into a 1
x' = dx/dx = 1 like any good fracation does :)
ooooooooo ok i see wat i did wrong
you got 3-y/Bx
omg im gonna do exactly wat u did for the test.. change that whole part to a B so i wont make a mistake
lol ..... it is easier on the eyes fer sure :)
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