1. ## Differentiation Problem

Hey. Have a question for my work, and need a little help getting the answer. Have been looking up the chain rule for some previous questions, but am now stuck, as i have not had one like this before. I'm not gonna give the actual question, as i want to work that out myself, but here is how it is styled:

differentiate 5x(9-3x)

so, normally that would be ok, but i havent had one with an x n the outside of the brackets, and am not sure what to do with it. Do i turn it into 5? but then that wouldn't make sense with the chain rule, so do i leave 5x as it is...

Help much appreciated.

Many thanks

2. Originally Posted by EternalChicken
Hey. Have a question for my work, and need a little help getting the answer. Have been looking up the chain rule for some previous questions, but am now stuck, as i have not had one like this before. I'm not gonna give the actual question, as i want to work that out myself, but here is how it is styled:

differentiate 5x(9-3x)

so, normally that would be ok, but i havent had one with an x n the outside of the brackets, and am not sure what to do with it. Do i turn it into 5? but then that wouldn't make sense with the chain rule, so do i leave 5x as it is...

Help much appreciated.

Many thanks
In this case just expand the brackets and the differentiate the quadratic
that results:

d/dx [5x(9-3x)] = d/dx [45x - 15 x^2] = 45 -30x

RonL

3. Ah, of course. Seems so obvious now :P

4. Originally Posted by EternalChicken
Hey. Have a question for my work, and need a little help getting the answer. Have been looking up the chain rule for some previous questions, but am now stuck, as i have not had one like this before. I'm not gonna give the actual question, as i want to work that out myself, but here is how it is styled:

differentiate 5x(9-3x)

so, normally that would be ok, but i havent had one with an x n the outside of the brackets, and am not sure what to do with it. Do i turn it into 5? but then that wouldn't make sense with the chain rule, so do i leave 5x as it is...

Help much appreciated.

Many thanks
Or you can think of this as a product:
d/dx[(5x)(9 - 3x)] = d/dx[5x]*(9 - 3x) + (5x)*d/dx[3 - 9x] = (5)*(9 - 3x) + (5x)*(-3)

= 45 - 15x - 15x = 45 - 30x

-Dan