(5x-y)^4 +4y^3 = 20704 solve for (2,-2) find the derivative

Question

jigglypuff314 · Answer

Hello and Welcome to OpenStudy!!! :)

I saw that you asked for help in the chat, maybe try adding the url link so that helpers can find it easier :)

I'm not very good at calculus, but I'll do my best to help :)

so I'm guessing you're confused by the fact that you're supposed to take the derivatives with ys involved?

anonymous · Answer

there are 2 
x and y

jigglypuff314 · Answer

the derivative of  y  is   y'  or   dy/dx

so   d/dx (5x - y)^4 =   (chain rule)
->  4(5x - y)^3 (5 - dy/dx)   or    4(5x-y)^3 (5-y' )

anonymous · Answer

ah ok ... would it be then 
4(5x-y)^ (5-y') + 12y^2

anonymous · Answer

plus the y' to the 12y^2*y'

jigglypuff314 · Answer

yes :)

anonymous · Answer

then you just plug in the points to solve for it

jigglypuff314 · Answer

yes :)
and know that  derivative of 20704 = 0

anonymous · Answer

im kind of confused at this part... bc when i plug it in 
it gives me a big number but doesn't make sense

jigglypuff314 · Answer

hmmm

4(5(2)-(-2))^3 (5-y') + 12(-2)^2 y' = 0

jigglypuff314 · Answer

4(5(2)-(-2))^3 (5-y') + 12(-2)^2 y' = 0
4(12)^3 (5-y') + 12(4) y' = 0
6921 (5-y') + 48 y' = 0
34560 - 6921 y' + 48 y' = 0

anonymous · Answer

yea for 4((5*2)-(-2)))^3 gives me = 6912

jigglypuff314 · Answer

oh yeah whoops that's right, typo on my part sorry

anonymous · Answer

thats exactly wat i got ... is that my answer

jigglypuff314 · Answer

you would solve for  y'

anonymous · Answer

ok thanks i got it!

jigglypuff314 · Answer

glad I could help :)

anonymous · Answer

maybe you could help me with this one ... im sorry lol 
would you do product rule or just go ahead a do the derivative 
2x^2-3xy+3y^3

jigglypuff314 · Answer

yeah... product rule for the  -3xy

anonymous · Answer

with 3y^3 right?

jigglypuff314 · Answer

huh?

anonymous · Answer

(-3y') * 3y^3 + (9y^2*y')* (-3xy) ?

jigglypuff314 · Answer

ermm... I'm slightly confused...
I got   4x - 3 - 3y' + 9y^2 y'

jigglypuff314 · Answer

whoops I meant
4x - 3y - 3xy' + 9y^2 y'

anonymous · Answer

ah ok ....  i was confused to wat im supposed to use the product rule to

anonymous · Answer

the derivative of -3xy is not -3*y'

jigglypuff314 · Answer

product rule

-3xy =  -3 (x*y)

derivative ->  -3 (y + xy')

anonymous · Answer

thanks you're really helpful

jigglypuff314 · Answer

you're welcome ^_^