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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

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

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

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'
oooooooooooooooooooo!!!!
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')?
or not...
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....
awwww!!! lol
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 :)
THANK U SOO MUCH!!!
UR A LIFE SAVER!!

Not the answer you are looking for?

Search for more explanations.

Ask your own question