Explanation:
This is the second fundamental theorem of calculus.
d/dx ∫ₐᵇ f(x) dx = f(b) (db/dx) − f(a) (da/dx)
This is derived using chain rule:
d/dx g(f(x)) = g'(f(x)) f'(x)
Therefore:
d/dx ∫₀²ˣ arctan(t) dt = arctan(2x) (2x)' = 2 arctan(2x)
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