Question

please answer this one
need step by step solution​

Answer 1

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

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