Implicit Differentiation Problem

[gerard.caleb]

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!

 

[sankalpmittal]

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.

 

[gerard.caleb]

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.

 

[sankalpmittal]

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.

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.