## d/dx cos^-1(u)

### To find the derivative of the function cos^-1(u) with respect to x, we can use the chain rule

To find the derivative of the function cos^-1(u) with respect to x, we can use the chain rule. Let’s write the function as arccos(u) to make it clearer. The chain rule states that if we have a composition of two functions, f(g(x)), then the derivative is given by the product of the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is arccos, and the inner function is u. So, the derivative can be calculated as follows:

d/dx arccos(u) = d(arccos(u))/du * du/dx

To differentiate the arccos(u) function with respect to u, we use the derivative identity:

d(arccos(u))/du = -1 / sqrt(1 – u^2)

And to differentiate u with respect to x, we simply obtain du/dx.

Combining these derivatives, we get:

d(arccos(u))/dx = (-1 / sqrt(1 – u^2)) * du/dx

So, the derivative of cos^-1(u) with respect to x is equal to (-1 / sqrt(1 – u^2)) times du/dx.

It’s important to note that we need to know the derivative of u with respect to x in order to compute the final result. If no information is given about u, then we can’t provide a more specific answer.

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