Final answer:
The correct answer is option B. The derivative of d/dx[arccot(x - √)] is found by applying the chain rule and results in -1/(1+x√), which corresponds to option B.
Step-by-step explanation:
The question asks about the derivative of the arccotangent function, specifically d/dx[arccot(x - √)]. To find this derivative, we need to apply the chain rule of calculus because the function includes a composition of functions. The derivative of arccot(u) with respect to u is -1/(1+u²). Here, u = x - √, so we need to take the derivative of u with respect to x as well.
In accordance with the chain rule, the overall derivative would be the product of the derivative of arccot(u) with respect to u and the derivative of u with respect to x. The derivative of arccot(u) is -1/(1+u²), and since u = x - √, the derivative of u with respect to x is 1. Therefore, the derivative of the overall function is -1/(1+(x - √)²). Simplifying this expression, we'll get option B) -1/(1+x √) as the correct result, keeping in mind any typographical errors in the original function notation.