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).
More Answers:
Understanding the Derivative of cot(x) with Respect to x: Step-by-Step Guide and Trigonometric IdentitiesMaster the Chain Rule: Derivative of the Arcsine Function Explained
How to Find the Derivative of the Arccos(x) Function Using the Chain Rule
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded