Derivatives - chain rule?

Question

i just learned bout chain rule but i still dont quite get it? especially like 'd/dx' wat is this thing?? thnx

Answer 1

let's say its da/dx means that you are taking derivates of a respect to x.

Answer 2

I would say dy/dx is a misleading way of writing, although it is a nice way. Actually, it should be
d
-- (y)
dx
meaning differentiate with respect to x for y or differenciate y with respect to x.

Thus, d/dx is an operation on to something, usually written besides the d on top (note not numerator, as the horizontal line has nothing to do with division).

So, in chain rule, e.g. y = 3u^2, u = 6x^3
d/dx (y)
= d/dx (3u^2)
= d/du (3u^2) * d/dx (u)
= 6u * d/dx (6x^3)
= 6(6x^3) * 18x^2
= 36x^3 * 18x^2
= 648x^5

Check:
y = 3u^2 = 3(6x^3)^2 = 3*6^2*x^6 = 108x^6
d/dx (y) = d/dx (108x^6) = 6*108x^5 = 648x^5

Answer 3

dy/dx is like the first principle rule only its the easier way.

sorry i dont knwo what you really want to know

Answer 4

quotient rule is u'v-uv' all divided by way of using v^2 so a million. (x+a million)+x divided by way of using (x+a million)^2 2. 2(x+a million)^(a million/2)-(2x - 7).5(x+a million)^(-a million/2) all divided by way of using (x+a million) 3. (x^2 + 3 )-2x^2 all divided by way of using (x^2 + 3 )^2 4. 3(3x^2 + 7)-6x(3x - 5) all divided by way of using (3x^2 + 7)^2

Answer 5

search in google