find dy/dx where (x-3y)^3=y+5?

Differentiating implicitly gives

3(x - 3y)^2*(1 - 3dy/dx) = dy/dx

3(x - 3y)^2 - 9(x - 3y)^2*dy/dx = dy/dx

3(x - 3y)^2 = (dy/dx)*(1 + 9(x - 3y)^2)

dy/dx = 3(x - 3y)^2/(1 + 9(x - 3y)^2)

You use the chain rule and the power rule and the fact that when you differentiate y, it must be multiplied by dy/dx because y is itself a function of x and so the chain rule has to be applied to it.

You will see that I agree with the answer two before mine.

dy/dx(x-3y)^3 * dy/dx(x-3y) * dy/dx y = dy/dx (y + 5)

which equals

[3] * [x-3y]^2 * [-3] * [y'] = y'

-9[x-3y]^2 [y'] = y'

Either you copied something wrong or i'm doing the problem wrong... anyways right now i don't have to see what i'm doing wrong... but this is the write process... hopefully you can figure it out... i'll check back later to see if something got it... write now i gotta go... feel free to email me or im me... good luck.

EDIT: The guy above is right... that's what i was doing wrong. I did not open the brackets but instead i used the chain rule. Anyways do it the way he said... and use my process. Say if it works out.

Differentiating in both sides, we get

3(x-3y)^2 . (1-3dy/dx) = dy/dx

Collecting dy/dx terms we get

dy/dx = (1/1+9(x-3y)^2 ) * 3(x-3y)^2

use the formula (a + b)^3 open the brakets.....collect all the "y" terms.....then take the derivative.....simple...

um lessee use implicit differentiation. The answer should be (3x^2 - 12xy + 9y^2 - 6x + 18y) / (-6x^2 + 18xy+18x - 54y - 1)

this may be able to be simplified...not sure...don't wanna do it.

Take log on both sides.3log(x-3y)=log(y+5).Then differentiate w.r.t. x.