d/dx arctan(x)
To find the derivative of arctan(x) with respect to x, we can use the chain rule
To find the derivative of arctan(x) with respect to x, we can use the chain rule.
The chain rule states that if we have a function f(g(x)), where f and g are both differentiable functions, then the derivative of f(g(x)) with respect to x is given by:
(d/dx) [f(g(x))] = f'(g(x)) * g'(x)
In this case, f(u) = arctan(u) and g(x) = x.
So, let’s start by finding the derivative of arctan(u) with respect to u.
(d/du) [arctan(u)] = 1 / (1 + u^2)
Now, we need to find the derivative of g(x) = x.
(d/dx) [x] = 1
Finally, we can plug these results into the chain rule formula:
(d/dx) [arctan(x)] = (d/du) [arctan(u)] * (d/dx) [x]
= 1 / (1 + u^2) * 1
= 1 / (1 + x^2)
Therefore, the derivative of arctan(x) with respect to x is 1 / (1 + x^2).
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