Find Derivative - Get Guidance Here

[npellegrino]

I am having difficulty figuring this one, any guidance will be appreciated.

 

[Cyosis]

We cannot guide you until you show us where you get stuck. What kind of methods have you tried to use so far?

 

[npellegrino]

This is what I have so far.

I believe i use this rule d/dx log a ^ u = 1/(lna)u

so ln = 1
a = ln
u = (1+e^sqrtX)/(2-e^cosx)

now i need to take the derivative of u, does e^sqrtX = e^sqrtX or is it e^sqrtX * derivative of sqrtX making it e^sqrtX * 1/2sqrtX

d/dx u =

 

[Cyosis]

I believe i use this rule d/dx log a ^ u = 1/(lna)u

This 'rule' makes no sense whatsoever.

now i need to take the derivative of u, does e^sqrtX = e^sqrtX or is it e^sqrtX * derivative of sqrtX making it e^sqrtX * 1/2sqrtX

This is also pretty hard to read. Yes \exp(\sqrt{x})=\exp(\sqrt{x}). This is no surprise since everything equals itself. What you probably mean is \frac{d}{dx}\exp(\sqrt{x})=\exp(\sqrt{x}). That is wrong since you have to use the chain rule therefore your second guess,\frac{d}{dx}\exp(\sqrt{x})=\exp(\sqrt{x}) \frac{1}{2 \sqrt{x}}, is correct.