Arctan

# Arctan - Math 17B Kouba Differentiating an Inverse Trig...

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Unformatted text preview: Math 17B Kouba Differentiating an Inverse Trig Function Trig Function Domain Restriction Inverse Function Derivative of Inverse y=tanm _£<\$<7r - t ’— 1 2 2 y—arcanx y_1+:c’ 1 Why is D arctanz = 1+1:2 PROOF : y = arctanaz => :1: = tany (Deﬁnition of inverse tangent) => 1 2 sec2 y - y’ (Implicit differentiation) => 3/ = sec; y (Solve for y.) => y’ = U—CE-sﬁ (Deﬁnition of secant) => y’ = cos2 y => 2/ = (cos y)? 2 1 2) y’ = (————) (Deﬁnition of cosine and Pythagorean Theorem from \/1+o:2 right triangle) 1 :1: tany=m=— wit-H01 ...
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