Question

Find the derivative of g(x) = 11arctan(1/x) for x > 0. Simplify your answer.

Answer 1

To find the derivative of g(x) = 11arctan(1/x), use the chain rule to find the derivative of f(x) = arctan(1/x) and then multiply it by 11. The derivative of g(x) is 11/x² * 1/(1+ (1/x)²).

Step-by-step explanation:

To find the derivative of g(x) = 11arctan(1/x), we can use the chain rule. Let's denote f(x) = arctan(1/x). The derivative of f(x) can be found using the chain rule, and then we can multiply it by the constant 11 to find the derivative of g(x).

1. Let's calculate the derivative of f(x) using the chain rule: f'(x) = (1/x²) * (1/(1+ (1/x)²))
2. Now, we can find the derivative of g(x) by multiplying the derivative of f(x) by 11: g'(x) = 11 * f'(x) = 11 * (1/x²) * (1/(1+ (1/x)²))

Therefore, the derivative of g(x) is g'(x) = 11/x² * 1/(1+ (1/x)²). This is the simplified answer.