Help with Derivative

FalconPUNCH! · #1 $Old$ December 6th, 2007, 11:25 PM

$F = \frac{mW}{mSin(X)+Cos(X)}$

I get to this:

$F' = \frac{(mW)'(mSinX+CosX)- (mW)(mCosX+(-SinX))}{(mSinX+CosX)^2}$

*Note*
m = constant
W = Variable

In case you need the actual problem in order to get the derivative here it is:

Quote:

1. An Object with weight W is dragged along a horizontal plane by a force acting along a roope attached to the object. If the rope makes an angle T with a plane, then the magnitude of the force is:

Where m is a constant called the coefficient of friction. For what value of T is F smallest?

I've tried to get the derivative but the equation gets messy and I can't solve for 0 to get the critical numbers I need. Please help with the derivative.

ticbol · #2 $Old$ December 7th, 2007, 01:10 AM

Why is F(m*sinT +cosT) = mW?

It should only be, F*cosT = mW
So,
F = mW / cosT
dF/dT = [cosT *0 -mW(-sinT)] / cos^2(T)
Set dF/dT to zero,
0 = mW(sinT) / cos^2(T)
0 = mW(sinT)
0 = sinT
T = arcsin(0) = 0 or pi
Therefore, the rope should be parallel to the floor for minimum F.