Finding Implicit Derivative of (x^2)/(a^2) + (y^2)/(b^2) = 1

[malorie]

Here is my problem:

(x^2)/(a^2) + (y^2)/(b^2) = 1

The directions are to find dy/dx implicitly.

The answer the book gives is:

-(b^2x)/(a^2y)

The answer I came up with is:

-b^3x(a-x)/a^3y(b-y)

Can anyone help me figure out what I did wrong?

Thanks and God bless!

 

[galactus]

Re: Finding an Implicit Derivative

It is actually not that bad. You aren't trying to integrate, are you?.

To avoid the quotient rule, rewrite as \(\displaystyle b^{2}x^{2}+a^{2}y^{2}=a^{2}b^{2}\)

Then, remembering that a and b are constants, we have \(\displaystyle 2b^{2}x+2a^{2}y\cdot\frac{dy}{dx}=0\)

Now, solve for dy/dx:

\(\displaystyle \frac{dy}{dx}=\frac{-2b^{2}x}{2a^{2}y}=\boxed{\frac{-b^{2}x}{a^{2}y}}\)

 

[malorie]

Re: Finding an Implicit Derivative

Thanks, galactus!