Question

How to differentiate
http://puu.sh/8thLl.png

Thankyou!

Answer 1

do you know product rule in differentiation ?

Answer 2

\(\large (fg)'= f'g+fg'\)

Answer 3

here
\(\large f= (x-a)^n\)
\(\large g= (x-b)^m\)

Answer 4

Can you explain the rule to me?

Answer 5

let me give you an example

say we need to find derivative of x e^x

here f =x, g = e^x
\((fg)' = f'g +fg' \\ (x e^x)' = (x)' e^x +x(e^x)' \)

Answer 6

its like, for 1st term, keeping one function as it, and differentiating other function,

then for 2nd term, keeping other function as it is and differentiating first function

Answer 7

so what is the final answer?

Answer 8

did you try it first? ?
what is the derivative of \((x-a)^n \quad and\\(x-b)^m ??\)

Answer 9

O.O

Answer 10

wait, so I get the differences of f'g and g'f and i add them?

Answer 11

get f' first! only then you'll get f'g
f is (x-a)^n, right ?
so whats f' = derivative of (x-a)^n = ...?

Answer 12

n(x-a)^n-1 right?

Answer 13

correct, what about
(x-b)^m ??
same formula

Answer 14

(x-b)^m * n(x-a)^n-1 + (x-a)^n * (x-b)^m-1
is that simplifyable??

Answer 15

the only thing missing is "m" in the second term!
and no, don't try to simplify, keep it as it is :)

Answer 16

where is the 'm' supposed to go in the second term?

Answer 17

\(\large (x-b)^m \times n(x-a)^{n-1} + (x-a)^n \times m (x-b)^{m-1}\)

Answer 18

OH YES I FOUND MY MISTAKE, THANKYOU SO MUCH FOR YOUR TIME! Much appreciated!

Answer 19

most welcome ^_^