Find y'' by implicit differentiation

In summary, the process of finding y'' by implicit differentiation involves first finding y' and then using the formula y'' = [(y^3)(-3x^2)-(-x^3)(3y^2)(y')]/(y^3)^2. Simplifying is not necessary, but learning LaTeX may make the equations easier to read.
  • #1
gillgill
128
0
Find y'' by implicit differentiation
x^4+y^4=1
i found that y'=-x^3/y^3
y''=[(y^3)(-3x^2)-(-x^3)(3y^2)(y')]/(y^3)^2
y''=[-3x^2(y^3)-(-x^3)(3y^2)(-x^3/y^3)]/y^6
then i am stuck...please help...thanks
 
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  • #2
You really hsould learn latex.

Anyway, you already have the second derivative.. simplifying isn't important.
 
  • #3
can anybody teach me latex then?
 
  • #4
Theres a readme on it in one of the forums, i think its general physics.
 
  • #5
Just read over quotations from those that use it.
 
  • #6
I don't think you need to simplify anything...
 
  • #7
It looks horrible with those minus signs.U could get rid of them.

Daniel.
 

Related to Find y'' by implicit differentiation

1. What is implicit differentiation?

Implicit differentiation is a technique used in calculus to find the derivative of an implicitly defined function, where the dependent variable is not directly expressed in terms of the independent variable. It is used to find the slope of a curve at a given point.

2. Why do we need to use implicit differentiation?

We use implicit differentiation when a function is not explicitly defined in terms of the independent variable. This commonly occurs when the dependent variable is present on both sides of the equation and cannot be easily isolated. Implicit differentiation allows us to find the derivative of such functions.

3. How do I find y'' using implicit differentiation?

To find y'', or the second derivative, using implicit differentiation, we follow the same steps as finding the first derivative. We differentiate both sides of the equation with respect to the independent variable, treating the dependent variable as a function of the independent variable. Then, we solve for y''.

4. Can implicit differentiation be used for any function?

Yes, implicit differentiation can be used for any function that is implicitly defined in terms of the independent variable. However, it may not be the most efficient method for functions that can be easily expressed explicitly in terms of the independent variable.

5. Is implicit differentiation the same as explicit differentiation?

No, implicit differentiation and explicit differentiation are two different techniques used to find derivatives. Explicit differentiation is used for functions that are explicitly defined in terms of the independent variable, while implicit differentiation is used for functions that are implicitly defined.

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