Question

The derivative of the func f(x)=cos⁻¹ (x)

Answer 1

The derivative of the function f(x) = cos⁻¹(x) is f'(x) = -1 / (sqrt(1 - x^2)).

Step-by-step explanation:

The derivative of the function f(x) = cos⁻¹(x), where cos⁻¹(x) represents the inverse cosine function, can be found using the chain rule.

Let u = cos⁻¹(x), then we have f(x) = u. To find the derivative of f(x), we differentiate u with respect to x and multiply by the derivative of x with respect to u.

Using the chain rule, the derivative of f(x) is: f'(x) = -1 / (sqrt(1 - x^2)).