Implicit Differentiation Question

In summary, the given equation, 2x^{3}-3x^{2}y+2xy^{2}-y^{3}=2, has a derivative of y'=\frac{-6x^{2}+6xy-2y^{2}}{-3x^{2}y+4xy-3y^{2}}. The text's solution has the opposite sign for each term, but both answers are correct as multiplying by \frac{-1}{-1} does not change the result. The person was initially unsure of their answer but realized their error after being reminded of this concept.
  • #1
biochem850
51
0

Homework Statement



2x[itex]^{3}[/itex]-3x[itex]^{2}[/itex]y+2xy[itex]^{2}[/itex]-y[itex]^{3}[/itex]=2

Homework Equations





The Attempt at a Solution



6x[itex]^{2}[/itex]-(6xy+3x[itex]^{2}[/itex]y')+(2y[itex]^{2}[/itex]+4xyy')-3y[itex]^{2}[/itex]y'=0

y'=[itex]\frac{-6x^{2}+6xy-2y^{2}}{-3x^{2}y+4xy-3y^{2}}[/itex]


My text's solution is the same answer but with every every term having the opposite sign.

I don't see my error and I'm trying to determine why my answer is incorrect.





 
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  • #2
Your answer is correct! Remember you can multiply by [itex]\frac{-1}{-1}[/itex] and the result is the same (multiplying by 1).
 
  • #3
scurty said:
Your answer is correct! Remember you can multiply by [itex]\frac{-1}{-1}[/itex] and the result is the same (multiplying by 1).

How did I not catch that?:redface:

Thanks!
 

FAQ: Implicit Differentiation Question

1. What is implicit differentiation?

Implicit differentiation is a method used in calculus to find the derivative of a function that is not explicitly stated, but rather is given in the form of an equation. It involves treating one variable as a function of the other variable and using the chain rule to find the derivative.

2. When is implicit differentiation used?

Implicit differentiation is used when a function is given in the form of an equation and cannot be easily solved for one variable. It is also useful when dealing with curves or surfaces that cannot be represented by explicit functions.

3. How is implicit differentiation different from explicit differentiation?

Explicit differentiation is used to find the derivative of a function that is expressed explicitly in terms of one variable. Implicit differentiation, on the other hand, is used to find the derivative of an equation where one variable is dependent on another variable.

4. What is the process of implicit differentiation?

The process of implicit differentiation involves treating one variable as a function of the other variable, differentiating both sides of the equation with respect to the independent variable, and then solving for the derivative. The chain rule is often used in this process.

5. What are the applications of implicit differentiation?

Implicit differentiation is used in many fields of science and engineering, including physics, economics, and engineering. It can be used to find rates of change, optimize functions, and solve optimization problems. It is also a fundamental concept in the study of curves and surfaces in multivariable calculus.

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