- #1

chwala

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- Homework Statement
- Find the second derivative, ##\dfrac{d^2y}{dx^2}## for the relation;

##x^2+y^4=10##

- Relevant Equations
- differentiation

Find text (question and working to solution here ...this is very clear to me...on the use of implicit differentiation and quotient rule to solution). I am seeking an alternative approach.

Now from my study we can also have; using partial derivatives...

##\dfrac{d^2y}{dx^2}=\dfrac{-1}{2y^3}+\left[\dfrac{-x}{2}⋅\dfrac{-3}{y^4}⋅\dfrac{-x}{2y^3}\right]##

##\dfrac{d^2y}{dx^2}=-\dfrac{1}{2y^3}-\dfrac{3x^2}{4y^7}##

##\dfrac{d^2y}{dx^2}=\dfrac{-2y^4-3x^2}{2y^7}##

##\dfrac{d^2y}{dx^2}=-\left[\dfrac{2y^4+3x^2}{2y^7}\right]##

your thoughts...any other approach is welcome guys...

the

##\dfrac{d^2y}{dx^2}=-\left[\dfrac{y+1.5x^2y^{-3}}{2y^4}\right]## ...just in case it is not visible enough...

Now from my study we can also have; using partial derivatives...

##\dfrac{d^2y}{dx^2}=\dfrac{-1}{2y^3}+\left[\dfrac{-x}{2}⋅\dfrac{-3}{y^4}⋅\dfrac{-x}{2y^3}\right]##

##\dfrac{d^2y}{dx^2}=-\dfrac{1}{2y^3}-\dfrac{3x^2}{4y^7}##

##\dfrac{d^2y}{dx^2}=\dfrac{-2y^4-3x^2}{2y^7}##

##\dfrac{d^2y}{dx^2}=-\left[\dfrac{2y^4+3x^2}{2y^7}\right]##

your thoughts...any other approach is welcome guys...

the

**text book solution**is;##\dfrac{d^2y}{dx^2}=-\left[\dfrac{y+1.5x^2y^{-3}}{2y^4}\right]## ...just in case it is not visible enough...

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