calculus

posted by Anonymous

Find
y''
by implicit differentiation.
3x3 + 4y3 = 1

1. Steve

3x^3 + 4y^3 = 1

9x^2 + 12y^2 y' = 0
y' = -3x^2/4y^2

now, using the quotient rule,

y'' = (-24xy^2 + 3x^2(8yy'))/ 16y^4
= (-3xy^2 + 3x^2yy')/2y^4
= -3x (y - xy')/2y^3

= -3x(y - x*(-3x^2/4y^2))/2y^3
= -3x(4y^3 + 3x^3)/8y^5

or, you can use implicit differentiation twice:

9x^2 + 12y^2 y' = 0
18x + 24y (y')^2 + 12y^2 y'' = 0
3x + 4y y'^2 + 2y^2 y'' = 0
2y^2 y'' = -(3x + 4y (y')^2)
y'' = -(3x + 4y (y')^2)/2y^2
= -(3x + 4y * 9x^4/16y^4)/2y^2
= -3x(4y^3 + 3x^3)/8y^5

Similar Questions

1. Math - Calculus Question.

hey can someone explain to me the relationship between the chain rule and implicit differentiation?
2. Calculus 1 - implicit differentiation

I do not understand implicit differentiation. One of the problems are: find y' by implicit differentiation xy+2x+3x^2=4. I would appreciate any help that can be offered.
3. Calculus 1 - implicit differentiation

I do not understand implicit differentiation. One of the problems are: find y' by implicit differentiation xy+2x+3x^2=4. I would appreciate any help that can be offered.
4. calculus; implicit differentiation

Use implicit differentiation to find the slope of the tangent line to the curve at the point (4,1) -1x^2 - 4xy + 3y^3 = -29 I differentiated both sides and solved for dy/dx and got 2x-4y/9y^2-4x. Then I plugged in X and Y and got -4/7 …
5. Calculus 1 Implicit differentiation

Help please help me understand what i am doing wrong in this problem! x^3+3x^2y+y^3=8 find dy/dx using implict differentiation. The answer is x^2+2xy -------- but i keep getting x^2y x^2+y^2 ----- x^2+y^2
6. calculus

Given y^4 -x^4=16 find and simplify d2y/dx2 using implicit differentiation. I got the first derivative which was x^3/y^3 and no im am stuck on using implicit differentiation for the second derivative part
7. Calculus

How do you use imlicit differentiation to differentiate e^(xy)?
8. Implicit differentiation calculus

PLEASE HELP , I DON'T UNDERSTAND find dy/dx by implicit differentiation a) xy + x^5y^2 + 3x^3 - 4 = 1 b) lny = cos x thank you
9. Calculus [Implicit Differentiation]

If √x+√y=10 and y(16)=36, find y'(16) by implicit differentiation. If somebody could please help me by explaining how to solve this problem ! Thank you (:
10. Calculus: implicit differentiation

Find dy/dx by implicit differentiation 1. x^3 -xy+ y^2= 7 The given answer is (y-3x^2)/ (2y-x), but I'm not getting it. 2. How would I do this one?

More Similar Questions