# differentiable functions

• Jan 10th 2010, 07:37 AM
alexandrabel90
differentiable functions
http://i752.photobucket.com/albums/x...0/IMG_4825.jpg

can some kind soul tell me what is this question asking and how to solve it?
• Jan 10th 2010, 08:00 AM
abender
The product rule for two functions is given by

$\displaystyle (f \cdot g)' = f' \cdot g + f \cdot g\$

Using induction, prove that for any $\displaystyle n\geq2$ number of functions, the generalized product rule (given to you) holds.

• Jan 10th 2010, 08:05 AM
alexandrabel90
may i know what does the LHS N look a like symbol from k=1 to n mean? this is the first time im seeing that symbol thats why.
• Jan 10th 2010, 08:16 AM
abender
$\displaystyle \mathbf{Z}^{+}$ represents the set of positive integers. 1, 2, 3, ...

$\displaystyle \mathbf{R}$ represents the set of real numbers.
1, 905, -763, 0.13244, 0, 2/5, anything that is real (read: not imaginary; no i)

$\displaystyle \sum$ represents "the sum of." So, $\displaystyle \sum_{k=1}^n x^k = x^1 + x^2 + x^3 + ... + x^n$

$\displaystyle \prod$ represents "the product of." So, $\displaystyle \prod_{k=1}^n x^k = x^1 \cdot x^2 \cdot x^3 \cdot ... \cdot x^n$
• Jan 10th 2010, 08:28 AM
alexandrabel90
http://i752.photobucket.com/albums/x...0/IMG_4826.jpg

this is how i have done it..but i got stuck as to how to continue from there..
• Jan 10th 2010, 08:30 AM
VonNemo19
Quote:

Originally Posted by abender
$\displaystyle \mathbf{Z}^{+}$ represents the set of positive integers. 1, 2, 3, ...

?$\displaystyle \mathbf{R}^{+}$? represents the set of real numbers.
1, 905, -763, 0.13244, 0, 2/5, anything that is real (read: not imaginary; no i)

$\displaystyle \sum$ represents "the sum of." So, $\displaystyle \sum_{k=1}^n x^k = x^1 + x^2 + x^3 + ... + x^n$

$\displaystyle \prod$ represents "the product of." So, $\displaystyle \prod_{k=1}^n x^k = x^1 \cdot x^2 \cdot x^3 \cdot ... \cdot x^n$

.
• Jan 10th 2010, 08:51 AM
alexandrabel90
how do you show that A(n+1) = 0 from my working and hence the equation is true by induction?
• Jan 10th 2010, 10:04 AM
abender
Quote:

Originally Posted by VonNemo19
.

oops, i was copy-pasting from the latex code above obviously...