# Thread: Implicit differentiation

1. ## Implicit differentiation

Here my question , for example x^2*y^2=0 when y=x=1, find d/dx, can I make the y^2 = x^2 and therefor change the equation to x^4=0 and differentiate for my x?

2. ## Re: Implicit differentiation

Originally Posted by Frozenboy11
Here my question , for example x^2*y^2=0 when y=x=1, find d/dx, can I make the y^2 = x^2 and therefor change the equation to x^4=0 and differentiate for my x?
That is an impossible example.
$\displaystyle x^2y^2=0$ when $\displaystyle y=x=1$ does not exist.

3. ## Re: Implicit differentiation

Ok my bad let said it is equal to some number so can I let y^2=x^2? When x=y=1?

4. ## Re: Implicit differentiation

Originally Posted by Frozenboy11
Ok my bad let said it is equal to some number so can I let y^2=x^2? When x=y=1?
If $\displaystyle y^2=x^2$ then $\displaystyle 2yy^{\prime}=2x$ or $\displaystyle y^{\prime}=\frac{x}{y}$.

SO?

5. ## Re: Implicit differentiation

Originally Posted by Plato
If $\displaystyle y^2=x^2$ then $\displaystyle 2yy^{\prime}=2x$ or $\displaystyle y^{\prime}=\frac{x}{y}$.

SO?
Here the full question

6. ## Re: Implicit differentiation

Yes, that is wrong. "At x= y= 1" does not mean that you can set x= y before taking the derivative. You have to take the derivative, with respect to y as (1, y) approaches (1, 1). So, because this is the partial derivative with respect to 1, you can set x= 1, making $\displaystyle f(x, y)= ln((1+2y)^2+ (2- y)^2+ 4y^2)$. Differentiate that and then set y= 1.