d/dx arctan(x)
To find the derivative of arctan(x), we can use the chain rule
To find the derivative of arctan(x), we can use the chain rule. The chain rule states that if we have a function of the form f(g(x)), where f(x) is a function of g(x), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) multiplied by g'(x).
In this case, we have f(x) = arctan(x) and g(x) = x. The derivative of f(g(x)) with respect to x is therefore f'(g(x)) multiplied by g'(x).
The derivative of arctan(x) with respect to x is given by:
f'(g(x)) = 1 / (1 + (g(x))^2)
g'(x) = 1
Therefore, the derivative of arctan(x) with respect to x is:
d/dx arctan(x) = (1 / (1 + x^2)) * (1)
Simplifying this expression, we get:
d/dx arctan(x) = 1 / (1 + x^2)
So, the derivative of arctan(x) with respect to x is 1 divided by 1 plus x squared.
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