Implicit Differentiation Problem

In summary, the conversation discusses a problem involving implicit differentiation, which has not been taught in class. The student used Wolfram Alpha to solve the problem but did not understand the process. The conversation includes a question about differentiating y2 with respect to x and a second question involving the chain rule.
  • #1
gerard.caleb
5
0

Homework Statement



The P(a,b) be a point on the curve √x + √y = 1. Show that the slope of the tangent P is -√b/a


Homework Equations



?

The Attempt at a Solution



Apparently this is an implicit differentiation problem, however we haven't learned or discussed implicit differentiation at all.

I ran it through wolfram alpha to help give an idea of what to do and got the answer I was supposed to, but looking at the process I don't understand it at all.

It's here: http://www.wolframalpha.com/input/?i=the implicit derivative of sqrt x + sqrt y = 1

Is there any other way to solve this? If not, can anyone explain the first few steps, or link me to the solution of a similar problem?
Thanks!
 
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  • #2
gerard.caleb said:

Homework Statement



The P(a,b) be a point on the curve √x + √y = 1. Show that the slope of the tangent P is -√b/a


Homework Equations



?

The Attempt at a Solution



Apparently this is an implicit differentiation problem, however we haven't learned or discussed implicit differentiation at all.

I ran it through wolfram alpha to help give an idea of what to do and got the answer I was supposed to, but looking at the process I don't understand it at all.

It's here: http://www.wolframalpha.com/input/?i=the implicit derivative of sqrt x + sqrt y = 1

Is there any other way to solve this? If not, can anyone explain the first few steps, or link me to the solution of a similar problem?
Thanks!

Yes, this is an implicit differentiation problem. You had not done it?

Ok, before we begin, let's see if you can do this. If you can, then you are ready to proceed.

You have to differentiate y2 with respect to x.

d(y2)/dx=_______________...

What will you write in this blank? Assume that y2 changes with x.
 
  • #3
Thank you for your response!

Nope, we haven't done much of anything. We've had a substitute this entire unit and unfortunately none of them have been able to teach us much beyond the first basic rules.

d(y^2)/dx= 1/2y ?
We haven't done anything using Leibniz notation either, so I'm sorry if that's incorrect.
 
  • #4
gerard.caleb said:
Thank you for your response!

Nope, we haven't done much of anything. We've had a substitute this entire unit and unfortunately none of them have been able to teach us much beyond the first basic rules.

d(y^2)/dx= 1/2y ?
We haven't done anything using Leibniz notation either, so I'm sorry if that's incorrect.

I'm afraid that is incorrect. :redface:

So I assume you have not done chain rule also. Let's take another try.

Let y=(x2+2)2
Then dy/dx=____________??

What will you write in the blank ?

Note: You have to find dy/dx without doing the expansion of y.
 

What is implicit differentiation?

Implicit differentiation is a method used in calculus to find the derivative of a function that is not expressed explicitly in terms of a single variable.

How is implicit differentiation different from explicit differentiation?

Explicit differentiation involves finding the derivative of a function that is expressed explicitly in terms of a single variable, while implicit differentiation involves finding the derivative of a function that is not expressed explicitly in terms of a single variable.

Why is implicit differentiation used?

Implicit differentiation is used when it is not possible or convenient to express a function explicitly in terms of a single variable. It is also used when the derivative of a function is needed, but the function cannot be solved for a single variable.

What are the steps for solving an implicit differentiation problem?

The steps for solving an implicit differentiation problem are: 1) differentiate both sides of the equation with respect to the variable of interest, treating all other variables as constants, 2) solve for the derivative, and 3) simplify the expression, if possible.

What are some common applications of implicit differentiation?

Implicit differentiation is commonly used in physics, engineering, and economics to model relationships between variables that cannot be expressed explicitly. It is also used in optimization problems, such as finding the maximum or minimum value of a function.

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