# Is there anyone who can differentiate this function, and then isolate the Q?

• May 25th 2010, 11:51 PM
JBroeng
Is there anyone who can differentiate this function, and then isolate the Q?
Hi

Can anyone help me differentiate this function with respect to Q, and then isolate the Q?

J(Q,r) = ((A*D)/Q) + H((Q/2) + r + M) + ((P*F(r)*D)/Q)

Thank you

JBroeng
• May 26th 2010, 12:06 AM
CaptainBlack
Quote:

Originally Posted by JBroeng
Hi

Can anyone help me differentiate this function with respect to Q, and then isolate the Q?

J(Q,r) = ((A*D)/Q) + H((Q/2) + r + M) + ((P*F(r)*D)/Q)

Thank you

JBroeng

Is H a constant or a function?

CB
• May 26th 2010, 02:16 AM
HallsofIvy
Quote:

Originally Posted by JBroeng
Hi

Can anyone help me differentiate this function with respect to Q, and then isolate the Q?

J(Q,r) = ((A*D)/Q) + H((Q/2) + r + M) + ((P*F(r)*D)/Q)

Thank you

JBroeng

Assuming H is a constant this is
$\displaystyle J(Q,r)= AD Q^{-1}+ HQ/2+ Hr+ HM+ PF(r)DQ^{-1}$
and can be easily differentiated using the power rule.
• May 26th 2010, 03:23 AM
JBroeng
Yes A, D, H, r, M, P is constants and F(r) is a function.
• May 27th 2010, 12:39 AM
JBroeng
Hi again

I know it might be a dum question but how do I differentiate (H*Q)/2?

I have totally forgotten how to differentiate a fraction.

JBroeng
• May 27th 2010, 01:54 AM
HallsofIvy
The derivative of Ax is A. (That's a linear function so the derivative is just the slope.)

The fact that A is a fraction is irrelevant: the derivative of $\displaystyle \frac{A}{2}Q$ with respect to Q is $\displaystyle \frac{A}{2}$.
• May 27th 2010, 06:30 AM
JBroeng
Thank you so much !!!
• May 31st 2010, 01:04 AM
JBroeng
Sorry but bother you again ...but can any of you see how they get from a to b?

a) Q^2 = (2(A+P*f(r))D)/H

b) Q = (P*D*f(r))/H

Thank you for helping me...

JBroeng
• Jun 2nd 2010, 04:29 AM
JBroeng
I have found the solution.....they differentiate the function with respect to Q and r , and isolate Q in both of those function.....Thank you for all your help...