Calculate the derivative: d/dt ∫[sint 1]cos(x^2)dx=?

Answer 1

g(t) = d/dt∫_a^u(t)f(x)dx = f(u(t))u'(t) by Second Fundamental Theorem of Calculus

f(x) = cos(x²), u(t) = sin(t) and a = 1 which is a constant, so doesn't matter.

g(t) = cos(sin²(t))cos(t)