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Question Number 129031 by oustmuchiya@gmail.com last updated on 12/Jan/21
Given that tan^(−1) x show that    (dy/dx) = (1/(1+x^2 ))
Giventhattan1xshowthatdydx=11+x2
Answered by MJS_new last updated on 12/Jan/21
y=arctan x  x=tan y  dx=(dy/(cos^2  y))  (dy/dx)=cos^2  y  cos y =(1/( (√(1+tan^2  y))))=^(y=arctan x) (1/( (√(1+x^2 ))))  ⇒  (dy/dx)=(1/(1+x^2 ))
y=arctanxx=tanydx=dycos2ydydx=cos2ycosy=11+tan2y=y=arctanx11+x2dydx=11+x2

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