Question

Cab someone help me understand....

Given: z=z(x,y)
find...
dz/dy partial if:
x^4+3xy^2+5z=sin(z)

Answer 1

alright for this treat everything as a constant except for Y

Answer 2

and if you are differentiating with z you have to put dz/dy and solve for that specific value. Or if you are in multivariable calculus there is a formula which is -Fy/Fz would give your answer

Answer 3

this is basically like implicit differentiation but with 2 variables and if you remember for one variable when you differentiated y you had to put dy/dx so same case applies

Answer 4

@hamza_b23 I love your straight explanation :)

Answer 5

thank you

Answer 6

do i use the formula then or do i differentiate with respect to y and when i get to z i put dz/dy??

sorry implicit differentiate i never understood...

Answer 7

use the formula if you like you would get same answer

Answer 8

so just differentiate with respect to z and y and take the negative quotient?

Answer 9

and do i set the equation to 0 or leave it as is?

Answer 10

if you are finding dz/dy the implicit for that is -Fy/Fz

Answer 11

so take the partial for y over the partial for z with negative as the coefficient

Answer 12

@drifta808 just follow hamza's instruction one step at the time!

Answer 13

( x^4 ) ' = ....

Answer 14

formula looks much easier lol

Answer 15

If it's much easier, why don't you post your solution here?

Answer 16

-(6xy)/5-cos(z)?

Answer 17

Good job, Very close :)

Answer 18

do i leave sin(z) on other side of equal sign? making it -(6xy)/5 = cos(z)

Answer 19

cant be right...

Answer 20

I'm unsure if you mistype or not, just a tiny little bit different?
z' = - 6xy/ ( 5z - cosz )

Answer 21

why is it 5z? and not 5? dont u take the derivative?

Answer 22

Since you take dz:
d (5z) = 5z dz/dy

Answer 23

that is what i dont understand...

Answer 24

That's how implicit work out!

Answer 25

Pretending take implicit dy/dx with z as y

Answer 26

z now is function of y, just as y is function of x!

Answer 27

ok thanks, gonna have to watch some videos on implicit differentiation.. forget everything about it during multivariable calc

Answer 28

Mee, too! I tend to forget so easily :(

Answer 29

ok, i still dont understand why dz/dy of 5z = 5z(dz/dy) i get the (dz/dy) part but doesnt the chain rule make it just 5 * (dz/dy)

Answer 30

its suppose to be 5*dz/dy

Answer 31

so the answer i put was right? its -6xy/(5-cos(z))?

Answer 32

6xy+5(dz/dy)-cos(z)(dz/dy)=0

dz/dy(5-cos(z))=-6xy

dz/dy=-6xy/(5-cos(z))
??

Answer 33

that the right way to solve this?

Answer 34

yeah your right bro

Answer 35

ah ok thanks alot man... other guy made me really confused there but now i know how to solve these.. thanks!

Answer 36

can u tell me if im doing another problem right?

Answer 37

its all good use the formula its really simple alright if you see dz/dy then its -Fy/Fz

Answer 38

yeah sure

Answer 39

yea i like the formula more too but its nice to know both and this next one is supposed to be a total differential...

Answer 40

f(x1,x2...,xn)=sin(x1+2x2+3x3+...+nxn)

Answer 41

i got cos(x1)+2cos(x2)+...+ncos(xn)

Answer 42

is that all it is?

Answer 43

so what are you doing differentiating that?

Answer 44

it says find the total differential...

Answer 45

O ok one min

Answer 46

and yes bro your absolutely right, but make sure you put in your deltax1 delta x2 ..... delta xn as well

Answer 47

did you get that? so your answer would just be cos(x1)deltax1+2cos(x2)deltax2+...+ncos(xn)deltaxn

Answer 48

delta is the triangle notation

Answer 49

oh sorry got distracted with another problem but ok that makes sense thanks!!! ready to destroy this test now haha

Answer 50

lmao goodluck do me a favourite and give me a medal in every post :P im trying to beat my friend lmao

Answer 51

haha for sure will do!

Answer 52

awesome goodluck

Answer 53

thanks... u 2