Find d^2y/dx^2 by implicit differentiation.

x^(1/3) + y^(1/3) = 4

I know that first you must find the 1st derivative & for y prime I got 1/3x^(-2/3) + 1/3y^(-2/3) dy/dx = 0

Then for dy/dx I got
dy/dx = [-1/3x^(-2/3)] / [1/3y^(-2/3)]

I think that from here I would use the quotient rule to find the second derivative?

1. 👍 0
2. 👎 0
3. 👁 393
1. simplify your first derivative before going further
notice you can divide each term by 1/3 to get

x^(-2/3) + y^(-2/3) dy/dx = 0
dy/dx = -x^(-2/3) / y^(-2/3)
= - y^(2/3)/x^(2/3)
= - (y/x)^(2/3)

d^2y/dx^2 = (-2/3) (y/x)^(-1/3) [( xdy/x - y)/x^2)

replace the dy/dx in the square bracket by (y/x)^2/3) and see what you get.

Still messy but a small improvement.

1. 👍 0
2. 👎 0
2. ggggggggggggggggggggg

1. 👍 0
2. 👎 0

## Similar Questions

1. ### HELP CALCULUS

Find dy/dx by implicit differentiation. tan−1(4x2y) = x + 3xy2

2. ### calculus

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

3. ### 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 (:

4. ### Calc

Find y'' by implicit differentiation. 5x2 + y2 = 3 y'' =?

1. ### Calculus 1

If 5x^2+5x+xy=2 and y(2)= -14 find y'(2) by implicit differentiation

2. ### calculus

Using 4x^2 - 9y^2 = 36 Find y by implicit differentiation and then solve the equation explicitly for y and differentiate to get y' in terms of x.

3. ### Calculus

Use implicit differentiation to find dz/dy for yz = ln (x+z) I am unsure of how to deal with the right side specifically.

4. ### Calculus

Find dy/dx by implicit differentiation: x^2-2xy+y^3 = c Thank you!

1. ### Math

use implicit differentiation to find the point where the parabola defined by x^2-2xy+y^2+4x-8y+20=0

2. ### Calculus

use implicit differentiation to find dy/dx if x^3+y^3=6xy

3. ### calculus

Find dy/dx by implicit differentiation. arctan(2x^2y)=x+4xy^2