How to Find the Derivative of tan^-1(u) with the Chain Rule

d/dx tan^-1(u)

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

To find the derivative of the function f(x) = tan^-1(u) with respect to x, we can use the chain rule. The chain rule states that if we have a composite function, then the derivative of the composite function is the derivative of the outer function multiplied by the derivative of the inner function.

In this case, u is a function of x, so we can write u(x). The function f(x) can be rewritten as f(u) = tan^-1(u).

Now, let’s find the derivative.

First, we take the derivative of f(u) with respect to u. The derivative of tan^-1(u) with respect to u is given by: d/du tan^-1(u) = 1 / (1 + u^2).

Next, we multiply this derivative by the derivative of u with respect to x (du/dx) to find the derivative of f(x) = tan^-1(u) with respect to x.

Therefore, d/dx tan^-1(u) = (1 / (1 + u^2)) * du/dx.

Note that du/dx represents the derivative of u(x) with respect to x. Depending on the specific form of u(x), you may need to apply additional differentiation rules to find this derivative.

Overall, the derivative of tan^-1(u) with respect to x is given by: d/dx tan^-1(u) = (1 / (1 + u^2)) * du/dx.

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