Implicit Differentiation

In summary, implicit differentiation is a mathematical technique used to find the derivative of a function that is not expressed in the form of y = f(x). It is used when a function is not explicitly given in terms of y, or when there are multiple variables and the derivative needs to be found with respect to only one of them. The process involves differentiating both sides of the equation with respect to the variable of interest, using the chain rule if necessary. Some common applications of implicit differentiation include physics, engineering, economics, and finance. When solving implicit differentiation problems, it is important to identify the variable of interest, use the chain rule when necessary, and simplify the resulting equation before solving for the derivative. It is also important to check the answer
  • #1
[SOLVED] Implicit Differentiation

-4x^2+3xy+4y^3=-328

This is at the point (1,3)


Homework Equations





The Attempt at a Solution



here is my work

-4x^2+3xy+4y^3=-328
-8x+3xy'+3y+12y^2y'=0
-8x+3y=-3xy'-12y^2y'
-8x+3y=[-3x-12y^2]y'
y'=(-8x+3y)/(-3x-12y^2)
plug in x=1,y=3 then solve and get
m=-12/67
can you find the error?
It would be very much appreciated
thank you.
 
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  • #2
Try plugging in your values for x and y again.
 
  • #3
hey thankx, i accidently posted this question twice.
 

What is implicit differentiation?

Implicit differentiation is a mathematical technique used to find the derivative of a function that is not expressed in the form of y = f(x). This means that instead of solving for y explicitly, the function is left in its implicit form, where x and y are both present.

Why is implicit differentiation used?

Implicit differentiation is used when it is not possible or convenient to express a function explicitly in terms of y. It is also used when a function has multiple variables and it is necessary to find the derivative with respect to only one of them.

What is the process of implicit differentiation?

The process of implicit differentiation involves differentiating both sides of the equation with respect to the variable of interest, using the chain rule if necessary. The resulting equation will be in terms of the derivative of y with respect to x, which can then be solved for to find the derivative.

What are some common applications of implicit differentiation?

Implicit differentiation is commonly used in physics and engineering to find rates of change in systems with multiple variables. It is also used in economics and finance to analyze relationships between variables.

What are some tips for solving implicit differentiation problems?

Some tips for solving implicit differentiation problems include carefully identifying the variable of interest, using the chain rule when necessary, and simplifying the resulting equation before solving for the derivative. It is also important to check your answer and make sure it makes sense in the context of the problem.

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