Derivative of arctan(x)
du/(1+u^2)
The derivative of arctan(x) can be found using the derivative formula for inverse functions:
If y = f⁻¹(x), then the derivative of y is given by dy/dx = 1 / dx/dy
Let y = arctan(x), then x = tan(y)
Taking the derivative of both sides with respect to x, we have:
1 = sec²(y) (dy/dx)
Solving for dy/dx, we get:
dy/dx = 1/ sec²(y) = 1/(1 + tan²(y))
Substituting back y = arctan(x), we get the final answer:
dy/dx = 1/(1 + x²)
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