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Step-by-step explanation:
- Given We need to find differential coefficient of sec(tan^-1 x)
- Now d/dx(sec x) = sec x tan x
- Also d / dx (tan^-1 x) = 1 / 1 + x^2
- Now let tan^-1 x = r
- So dy / dx = d/dx (sec r)x.dr / dx (since chain rule)
- So sec r tan r x d/dx (tan^-1 x)
- So sec r tan r x 1 / 1 + x^2 ---------------1
- Now sec^2 r = 1 + tan^2 r
- So sec r = √1 + x^2
- Substituting this value in 1 we get
- √1 + x^2 x x 1 / (√1 + x^2)^2
- = x / √1 + x^2
Reference link will be
https://brainly.in/question/9491841
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