I need to find the stationary points of the following function:

g(x)=

e^((−3x+2sinx)/6)
------------------
(3+2cosx)

Question

I need to find the stationary points of the following function:

g(x)=

e^((−3x+2sinx)/6)
------------------
        (3+2cosx)

anonymous · Answer

take the derivativ ,make it equal to 0 and solve for x

anonymous · Answer

Got that point but have not been have follow through from the derivative to solve for 0

anonymous · Answer

Finding it difficult to solve trig function

anonymous · Answer

$$[(-3*2cpsx*e ^{-3x+2sinx/6}*3+2cosx)+(e ^{-3x+2sinx/6}*2sinx)]/(3+2cosx)^{2}$$
this is the derivative

anonymous · Answer

Ok. I have got this point but find it to make it come out to 0 and therefore find the stationary points

anonymous · Answer

It difficult to get it to 0

anonymous · Answer

I can't simplify it enough

anonymous · Answer

I assume that it means solving the numerator only?

anonymous · Answer

taking out the exponential:
$$e ^{-3x+2sinx/6}(2sinx-6cosx(3+2cosx)) =0$$

anonymous · Answer

you right about the numerator, becouse the denominator is never 0

anonymous · Answer

Great. Really helps to know that fact.

anonymous · Answer

so: 2sinx-18cosx-12cos^2x=0 solve this

anonymous · Answer

How did you get to this point from what you wrote previously? Where is the exp gone?

anonymous · Answer

exponential also doesn't mater, becouse its never 0

anonymous · Answer

I am trying to solve it. WIll be back soon with the answer. Thanks,

anonymous · Answer

$$1/y^(5/6)$$