So in my calculus class we learned about implicit differentiation today. The professor would stop and ask if we had any questions, which was nice. I didn't ask any questions though, because I don't really like to ask questions during class. I didn't really get implicit differentiation today though. Do you think I should stop by the professor's office during the professor's office hours and let the professor know that I didn't really get it? Or no? Do you think the Professor would be mad or frustrated or concerned if I told the Professor I didn't get it?

Answer 1

Definitely, ask the professor about this. He might be mad. But more likely, he'll admire you for asking --even if it is late.

Before you talk with him, though, I suggest you try to find out about differentiation in your book or online.

Answer 2

A good rule of thumb is, that if you have a question, there are others who do also. Evidently they were also too shy to ask it, so you should.

the teacher knows this, too, so he'd be much happier if someone (you!) asks the question, since it's easier to explain it to a group all at once than to have to do it several times in his office.

Implicit differentiation is really just a way to use your chain rule and product rule.

You know that if

y = uv
then
dy/dx = du/dx * v + u * dv/dx

So, suppose you have

x^2y + 2xy^3 = 17x - 3y

the product rule says that

(2x dx/dx)y + x^2 (dy/dx) + 2(dx/dx)y^3 + (2x)(3y^2 dy/dx) = 17 dx/dx - 3 dy/dx

Since dx/dx = 1 and dy/dx = y', that is just

2xy + x^2y' + 2y^3 + 6xy^2y' = 17 - 3y'
Now collect all the y' stuff on the left, and you have

y'(x^2+6xy+3) = 17-2xy-2y^3
so,

y' = (17-2xy-2y^3)/(x^2+6xy+3)

No matter how complicated it looks, the same basic steps always apply.

Why is the derivative of ln x = 1/x?

y = lnx
e^y = x
e^y y' = 1
y' = 1/e^y = 1/x