# Implicit Differentiation concept help?

• shocklightnin
In summary, the conversation was about implicit differentiation and finding the equation of a tangent line at a given point. The poster initially struggled with understanding the steps used by their professor, but eventually figured it out with the help of the product rule. They considered deleting the thread after their question was answered, but decided to leave it as it may help others in a similar situation.
shocklightnin

## Homework Statement

Its not homework, i have the answer I am just having a hard time wrapping my head around the concept of differentiating implicitly defined functions.

the question was: x^3+y^3=3xy, find the equation of the tangent line at the point (3/2,3/2).

x^3+y^3=3xy

## The Attempt at a Solution

so what my prof did was:
1)x^3+y^3=3xy
2)3x^2+3y^2(dy/dx)=3y+3x(dy/dx)

i get the part on the left, but i don't understand how he got the part on the right... :/

if anyone could just elaborate on the steps in between those two it would be much appreciated for my understanding. thank you.

ah nevermind I got it, silly really. how can i delete this thread?

Your prof used the product rule on the right side.

yeah. i feel extremely silly for asking. I've been staring at the screen for too long at these examples. any way to delete this cause its 'solved'? or do i just sort of leave it.

shocklightnin said:
yeah. i feel extremely silly for asking. I've been staring at the screen for too long at these examples. any way to delete this cause its 'solved'? or do i just sort of leave it.

Oh, just leave it. It's no big deal. Everybody has their silly moments. Sometimes just posting a question helps you think.

Yeah, typing it out defs helped. Alright, just going to leave it then.

## What is implicit differentiation?

Implicit differentiation is a mathematical concept used to find the derivative of a function that cannot be easily expressed in terms of a single variable. It involves treating one variable as a function of another variable and using the chain rule to find the derivative.

## When is implicit differentiation used?

Implicit differentiation is used when a function cannot be easily solved for one variable in terms of another. It is commonly used in advanced calculus and physics, and is particularly helpful in finding the derivatives of equations involving multiple variables.

## How is implicit differentiation different from explicit differentiation?

Explicit differentiation involves finding the derivative of a function in terms of a single variable, while implicit differentiation involves finding the derivative of a function that cannot be expressed in terms of a single variable. Implicit differentiation is more complex and often requires the use of the chain rule, while explicit differentiation is more straightforward.

## What are the steps for performing implicit differentiation?

To perform implicit differentiation, you first need to identify the dependent and independent variables in the equation. Then, you apply the chain rule to find the derivative of the dependent variable with respect to the independent variable. Finally, you solve for the derivative and simplify as needed.

## Why is implicit differentiation important in science?

Implicit differentiation allows us to find the derivative of functions that are too complex to solve using traditional methods. This is important in science because many natural phenomena and physical laws can be described using complex equations, and implicit differentiation allows us to better understand and analyze these systems.

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