Unformatted text preview: Math 17B
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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—CEsﬁ (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=—
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 Winter '07
 Kouba

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