Question

Can any1 explain the 3 theorems of differentiation?? pls pls

Answer 1

The 1 that says if y = f(x) and k is a constant then dy/dx = k*df(x)/dx and the rest!!!!!!!

Answer 2

pls explain!!!!!!

Answer 3

This is basically saying that the derivative of a constant times a function is that same constant times the derivative of the function. So, if you have \[f(x)= 4x^{2}\]
and you want the derivative \[f'(x)= 4x^{2}dx\]
it is the same as
\[4f'(x)= x^{2}dx\]

Answer 4

pls explain the other 2

Answer 5

I don't know the other two off the top of my head. If you post them I may be able to explain them.

Answer 6

the 1 that says if y = u(x) + v(x) + w(x) then y' = u'(x) + v'(x) + w'(x)

Answer 7

The derivative of a sum of functions is the sum of the derivatives of the functions.

Answer 8

?

Answer 9

does u'(x) mean that it is the derivative of u(x)??????

Answer 10

Yes, that is a common way of indicating derivative, along with d/du, etc.

Answer 11

so if we were to write u(x) in its dy/dx form then it will still remain du/dx??

Answer 12

I'm not sure I understand the question. in your statement above, "y = u(x) + v(x) + w(x) then y' = u'(x) + v'(x) + w'(x)", I assumed that u, v, and w are all some function of x. Thus u', v', w' are all derivatives of those functions with regard to x.

Answer 13

its just notation; there are many ways to express it

Answer 14

u' ; du/dx ; Dx; etc