Question #52b72

1 Answer
Layth A.
Feb 14, 2018

By using the common derivative arccot formula and the chain rule, we get alpha/(alpha^2+x^2)

Explanation:

For the given problem:

y=arccot(alpha/x)

We must apply a common derivative formula of:
d/dx(arccot(u))=-1/(u^2+1)

and the chain rule (this is only because our "u" is something other than just x)

  1. in our problem we assign the following for ease:
    f=(arccot(u))
    u=alpha/x

  2. our derivative will be:
    =d/(du)(arccot(u))*d/dx(alpha/x)

  3. We can then calculate them separately and simplify:
    d/(du)(arccot(u)) = color(red)(-1/((alpha/x)+1))
    d/(dx)(alpha/x)=alpha*d/(dx)1/x=alpha*d/(dx)x^-1=color(blue)(-alpha/x^2)

  4. Multiply together and simplify
    color(red)(-1/((alpha/x)+1)) * color(blue)(-alpha/x^2)

For a final answer of:
=alpha/(alpha^2+x^2)

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