Question

Can someone help me find derivative of y?

Answer 1

Ive attached the question and I found the value of k= -3 but I can solve the second part of the problem which is find the derivative of y

Answer 2

presume you can do the 2nd and 3rd terms? ie that your prpb is with first term exp(xy^2)?

Answer 3

The answer is y'=-1/4 if that helps

Answer 4

i thought you wanted to know how to do it? can you do any of it yourself?

Answer 5

I do want to know, thats the answer in the back of the book

Answer 6

what i mean is that the answer right now is not that important. the method is important.

Answer 7

Would -2x = -2dy/dx?

Answer 8

-4y=-4

Answer 9

k = 0

Answer 10

other way round

d/dx ( -2x) = -2

d/dx (- 4y) = -4 dy/dx

Answer 11

\[e ^{xy ^{2}}=e ^{xy ^{2}}(y ^{2} * 2xy)?\]

Answer 12

nah, but i see what you are trying to do.

can you calculate d\dx (xy^2) ? looking at the previous 2 derivatives we calculated and sticking with your use of the product rule?.

Answer 13

you are very close BTW

Answer 14

Ok, \[d/dx(xy^2) = y^2 +2xy (\frac{ d }{ dx }) \]

Answer 15

Is that correct?

Answer 16

that last term you wrote as (d/dx) should be dy/dx. agree?

Answer 17

Because we are taking the derivative of Y with respect to X?

Answer 18

yep!

Answer 19

But the question ask to find the derivative of Y, so I'm confused shouldn't it be the other way around?

Answer 20

How do you remember which way to write it/do it based on what the question is asking? Haha what's your trick?

Answer 21

I mean we are finding the derivate of y why do we do dy/dx to y? My logic is that we should do dx/dy to x ... :S

Answer 22

x is the fundamental underlying variable and y is just a function of x, ie y = f(x). so everything is ultimately about x.

think chain rule, if that helps.

d/dx(x^2) is the rate of change of (x^2) wrt x, ie 2x. d/dx (y^2) is the rate of change of (y^2) wrt x, ie 2y dy/dx. or d/dy (y^2) • dy/dx.

Answer 23

anyways we are close to putting this to bed.

Answer 24

your move!

Answer 25

Btw I got the correct answer thanks!

Answer 26

oh! you finished it?!?!

Answer 27

Haha thanks and I understand the logic a little bit better now

Answer 28

no seriously, that's great. well done.

Answer 29

So if there was no y=f(x) then x would not be a fundamentally underlying variable and we would do it differently?

Answer 30

and -2x(d/dy) would be a thing?

Answer 31

yes, we would use partial derivatives, ie we would be looking at x and y as truly independent variables. though calculus is such a magical world that we could use partial derivatives and then connect them back later and solve this is a different way. and if they are independent, how can they live in the same equation that does not have a further variable connecting them?!

PS: -2x (d/dy) doesn't mean anything to me. d()/dx and d/dx () are magical mathematical *functions* - i'll get shouted at for saying that but it is largely true. they take the thing in the brackets and tell you how it changes wrt x. if there is now't in brackets, the function has no argument.

Answer 32

OK!!!!! thats amazing haha thanks for the explanation @IrishBoy123! You learn something new everyday and this was interesting knowledge.

Answer 33

me too dude.

Answer 34

So d()/dx and d/dx () are different things right