## d/dx[(cosx)^-1]

### To find the derivative of the function f(x) = (cosx)^-1, we will use the chain rule

To find the derivative of the function f(x) = (cosx)^-1, we will use the chain rule.

The chain rule states that if we have a composite function g(f(x)), then the derivative of g(f(x)) is given by g'(f(x)) multiplied by f'(x). In this case, g(u) = u^-1 and f(x) = cosx.

Let’s differentiate the function step by step:

First, we need to find f'(x), which is the derivative of the inner function f(x) = cosx. This is given by f'(x) = -sinx.

Next, we differentiate g(u) = u^-1 with respect to u. Using the power rule of differentiation, we have:

g'(u) = -(1/u^2).

Now, by applying the chain rule and multiplying g'(f(x)) by f'(x), we get:

(d/dx)(cosx)^-1 = -(1/(cosx)^2) * (-sinx)

Simplifying this further, we have:

(d/dx)(cosx)^-1 = sinx / (cosx)^2

Therefore, the derivative of the function f(x) = (cosx)^-1 is sinx / (cosx)^2.

##### More Answers:

Understanding and Solving for the Derivative of the Inverse Cosine Function | Step-by-Step GuideHow to Find the Derivative of the Arcsin Function

The Derivative of f(x) = (tanx)^-1 Using the Chain Rule for Differentiation