1. ## [SOLVED] Implicite differentiation

I'm having so much difficulty with this. The techniques used by my teacher are very difficult for me to grasp. Last semester I failed calculus and I didn't understand this part either. The rest of the material I understand better but this one subject is making it very difficult for me to solve related rates problems.

For example, I know some formulas for related rate problems but I cannot get them on my own and so sometimes when they ask for just one type of formula I'm stuck because I cannot crack the code so to speak.

I could really use some help in understanding this subject better. Thanks.

2. Originally Posted by thekrown
I'm having so much difficulty with this. The techniques used by my teacher are very difficult for me to grasp. Last semester I failed calculus and I didn't understand this part either. The rest of the material I understand better but this one subject is making it very difficult for me to solve related rates problems.

For example, I know some formulas for related rate problems but I cannot get them on my own and so sometimes when they ask for just one type of formula I'm stuck because I cannot crack the code so to speak.

I could really use some help in understanding this subject better. Thanks.

3. 4x^2 + 6xy + 7y^2 + 11y - 4 = 0

I'm fairly good at derivatives but the second I have to do this with a y as well it's like a mack truck hitting me in the face. I've tried using my online math helper as well and my brain just can't process it.

There must be some key piece of understanding that I don't have to be able to see how this is done.

4. Originally Posted by thekrown
4x^2 + 6xy + 7y^2 + 11y - 4 = 0

I'm fairly good at derivatives but the second I have to do this with a y as well it's like a mack truck hitting me in the face. I've tried using my online math helper as well and my brain just can't process it.

There must be some key piece of understanding that I don't have to be able to see how this is done.
The derivative of 4x^2 wrt x is trivial.

The derivative of 6xy wrt x is found using the product rule: $\displaystyle 6y + 6x \frac{dy}{dx}$.

The derivative of y^2 wrt x is found using the chain rule: $\displaystyle \frac{d (y^2)}{dx} = \frac{d (y^2)}{dy} \cdot \frac{dy}{dx} = 2y \, \frac{dy}{dx}$.

The derivative of y wrt x is obviously $\displaystyle \frac{dy}{dx}$.

The derivative of 4 is zero.

So differentiate the given relation with respect to x, substitute the above expressions and make dy/dx the subject.