Differentiation with trig functions

[Asphyxiated]

Homework Statement

An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle θ with the plane, then the magnitude of the force is given by the following equation, where μ is a constant called the coefficient of friction.

$$F = \frac {\mu W} {\mu sin(\theta) + cos(\theta)}$$

Find the rate of change of F with respect to theta.

Homework Equations

Quotient Rule for Differentiation

$$\frac {d}{dx} \frac {f(x)}{g(x)} = \frac {g(x)*f'(x)-f(x)*g'(x)}{(g(x))^{2}}$$

The Attempt at a Solution

So i assumed that μW is the same as something like 2x so I took its derivative to be μ and I think that's all I need to explain so...

$$\frac {dF}{d\theta} = \frac { (\mu sin(\theta) + cos (\theta))(\mu) - (\mu W) (\mu cos (\theta)-sin(\theta))} { (\mu sin(\theta) + cos (\theta))^{2}}$$


$$\frac {dF}{d\theta} = \frac {\mu^{2} sin(\theta) + \mu cos (\theta) - (\mu^{2}Wcos(\theta)-\mu W sin(\theta))} { (\mu sin(\theta) + cos (\theta))^{2}}$$


$$\frac {dF}{d\theta} = \frac {\mu^{2} sin(\theta) + \mu cos (\theta) - \mu^{2}Wcos(\theta)+\mu W sin(\theta)} { (\mu sin(\theta) + cos (\theta))^{2}}$$

Thats what I get, which is wrong according to the program we use for my class but it will never tell me what the right answer is so I am kind of at a loss here until monday unless someone can point out where I went wrong. I also re-did it while assuming μW to be a total constant with a derivative of just 1 and the only thing that changes is then:

$$\frac {dF}{d\theta} = \frac {\mu sin(\theta) + cos (\theta) - \mu^{2}Wcos(\theta)+\mu W sin(\theta)} { (\mu sin(\theta) + cos (\theta))^{2}}$$

Which is also wrong... thanks for any help in advance!

 

[fzero]

I also re-did it while assuming μW to be a total constant with a derivative of just 1

The derivative of a constant is 0.

 

[Asphyxiated]

heh... yes it is, that's funny... i wonder where i got the 1 from... anyway that fixes it... thanks for pointing out my dumb mistake