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Question

Differentiate the following functions w.r.t.x
tan1(1+a2x2ax)

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Solution

Let y=tan1(1+a2x2ax)
tany=1+a2x2axtan2y=1+a2x2a2x2
a2x2tan2y=1+a2x2 by squaring both sides
a2x2(tan2y1)=1
a2[x22tanysec2ydydx+2x(tan2y1)]=0
2a2x2tanysec2y.dydx=2x(1tan2y)
a2x1+a2x2axsec2ydydx=11+a2x2a2x2
a1+a2x2(1+tan2y)dydx=a2x21a2x2a2x2
(1+1+a2x2a2x2)dydx=1a2x2×a1+a2x2
2a2x2+1a2x2dydx=1a2x2×a1+a2x2
dydx=1a2x2×a1+a2x2
dydx=1a2x2×a1+a2x2


1218713_1365606_ans_0a9a315a028a4d0aab7076753734855f.PNG

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