# Simple Derivative

• Jul 15th 2007, 11:29 PM
Jimpson
Simple Derivative
Hello,

I'm a bit rusty on my calculus and I have this function and when I use the chain rule I get the f'(x) function

http://img179.imageshack.us/img179/382/untitled1qx1.gif

I must be doing something wrong though as when x = 9.17, the dy/dx value should be about 16 but it ends up being about .33 something. Can anyone point out where I went wrong? Thanks in advance.
• Jul 15th 2007, 11:37 PM
Jhevon
Quote:

Originally Posted by Jimpson
Hello,

I'm a bit rusty on my calculus and I have this function and when I use the chain rule I get the f'(x) function

http://img179.imageshack.us/img179/382/untitled1qx1.gif

I must be doing something wrong though as when x = 9.17, the dy/dx value should be about 16 but it ends up being about .33 something. Can anyone point out where I went wrong? Thanks in advance.

how did you get 75 in the top?

obviously you're using the quotient rule incorrectly.

recall:

Quotient Rule:

$\left( \frac {u}{v} \right)' = \frac {vu' - uv'}{v^2}$
• Jul 15th 2007, 11:45 PM
Jimpson
Quote:

Originally Posted by Jhevon
how did you get 75 in the top?

150 * (1+49.1e^-.5x)^-1

-150 * (1+49.1e^.5x)^-2 * -.5e^.5x

75e-.5x
(1+49.1e^.5x)^2

If that makes sense.
• Jul 15th 2007, 11:53 PM
Jimpson
Quote:

Originally Posted by Jhevon
how did you get 75 in the top?

obviously you're using the quotient rule incorrectly.

recall:

Quotient Rule:

$\left( \frac {u}{v} \right)' = \frac {vu' - uv'}{v^2}$

I thought quotient rules were used for a function on both the top and bottom of the fraction?
• Jul 15th 2007, 11:54 PM
Jhevon
Quote:

Originally Posted by Jimpson
150 * (1+49.1e^-.5x)^-1

-150 * (1+49.1e^.5x)^-2 * -.5e^.5x

75e-.5x
(1+49.1e^.5x)^2

If that makes sense.

ok, so you used the product rule. but note that you have the wrong derivative for the inside.

the derivative of 1 + 49.1e^{-0.5x} is -24.55e^{-0.5x}, there's your problem.

remember, you have a constant 49.1 multiplying the e
• Jul 15th 2007, 11:55 PM
Jhevon
Quote:

Originally Posted by Jimpson
I thought quotient rules were used for a function on both the top and bottom of the fraction?

well, technically a constant is a function. it will work anyway. you can use the product rule if you wish, i gave you the corrections already
• Jul 16th 2007, 12:00 AM
Jimpson
Quote:

Originally Posted by Jhevon
ok, so you used the product rule. but note that you have the wrong derivative for the inside.

the derivative of 1 + 49.1e^{-0.5x} is -24.55e^{-0.5x}, there's your problem.

remember, you have a constant 49.1 multiplying the e

Ahh, of course, thanks a bunch mate! :D