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differentiate tan^-1(1+ax/1-ax) with respect to sqrt(1+a^2x^2)

differentiate tan^-1(1+ax/1-ax) with respect to sqrt(1+a^2x^2)

Grade:12

3 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hi


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Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

kantha mani
27 Points
6 years ago
Let x = (1/a) tan yThen, u = tan^1 [(1 + tan y)/(1 - tan y)] = tan^1 [(tan pi/4 + tan y)/(1 - tan pi/4 tan y)] = tan^1 [tan (pi/4 +y)] = (pi/4 + y) = pi/4 + tan^1(ax)du/dx = 1/(1+a^2x^2)v = (1 + a^2x^2)^1/2dv/dx = a^2x/ ( (1 + a^2x^2)^1/2du/du = 1/a^2x (1 + a^2x^2)^1/2
kantha mani
27 Points
6 years ago
Let x = (1/a) tan yThen, u = tan^-1 [(1 + tan y)/(1 - tan y)] = tan^-1 [(tan pi/4 + tan y)/(1 - tan pi/4 tan y)] = tan^-1 [tan (pi/4 +y)] = (pi/4 + y) = pi/4 + tan^-1(ax)du/dx = 1/(1+a^2x^2)v = (1 + a^2x^2)^1/2dv/dx = a^2x/ ( (1 + a^2x^2)^1/2du/du = 1/a^2x (1 + a^2x^2)^1/2

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