We started today by finishing the batter problem and determining the distance at which the batter can no longer track the incoming baseball. (Slide 1)
The we solved a few derivative and integral problems that featured inverse trigonometric functions. We eventually derived a formula for inverse secant. The absolute value is there because of the definition of y = sec^(-1)(x). The function is always increasing over its entire domain.
The last problem involved the derivative of the inverse cot function. We solved it by deriving a formula and then applying it to the specific case. Alternatively, we could have used the relationship cot^(-1)(x) = tan(-1)(1/x) and used the inverse tan derivative formula. You should try this.
You should also try deriving all of the derivative formulae for the inverse trig functions using the general relationship between the derivative of any inverse functions. Do you remember it?
d/dx(f^(-1)(x)) = 1 / f'(f^(-1)(x))
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Review sheet # 2 should be started (finished?) over the weekend.
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