finding dy/dx ie. the derivative of this complicated function

[avanm]

Hello all!

This is a bonus question on my assignment that I have no idea how to do. I will refer to the parts of the equation by 1, 2, 3. 1 being the first function, 2 bring the second and the third being the arctan giant function.
I began by doing d/dx of 1 using quotient rule. I got 1/sqrt(a^2+1)
then 2 and 3 are quotient rule do d/dx (2) ∗ (3) + d/dx (3) ∗ (2) d/dx(2)= 0

I'm finding trouble in deriving the (3) part.

If anyone can help me derive this that would be appreciated

 

[Steven G]

Why would you use the quotient rule for 1?!! sqrt(a^2 + 1) is a constant, so the derivative of x/(sqrt(a^2+1)) is simply [derivative of x]/(sqrt(a^2+1) which is 1/ sqrt(a^2+1).

The answer will be in the form of 1/ sqrt(a^2+1) - [2/(sqrt(a^2+1)]* derivative [ arctan (sinx/(a+sqrt(a^2-1) + cosx)]

Now finish up by computing the derivative of [ arctan (sinx/(a+sqrt(a^2-1) + cosx)]

What is d/dx (arctan u) and what is u in your case???

 

[avanm]

Why would you use the quotient rule for 1?!! sqrt(a^2 + 1) is a constant, so the derivative of x/(sqrt(a^2+1)) is simply [derivative of x]/(sqrt(a^2+1) which is 1/ sqrt(a^2+1).

The answer will be in the form of 1/ sqrt(a^2+1) - [2/(sqrt(a^2+1)]* derivative [ arctan (sinx/(a+sqrt(a^2-1) + cosx)]

Now finish up by computing the derivative of [ arctan (sinx/(a+sqrt(a^2-1) + cosx)]

What is d/dx (arctan u)???

right! yes thats what im having trouble deriving the arctan part

 

[Steven G]

right! yes thats what im having trouble deriving the arctan part

OK, so show us what you did so we can offer you some help. Can you answer my question as to what is d/dx (u)?? That will be a start.

 

[Deleted member 4993]

right! yes thats what im having trouble deriving the arctan part

What does your text-book say? Did you try Google?