The derivative of  with respect to tan-1x is:

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AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper
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Option 2 :
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Given:

The derivative of  with respect to tan-1x is:

Concept:

The derivative of f(x) with respect to g(x) is 

Calculation:

Let  and g(x) = tan-1x

Put x = tanθ in f(x) then

On differentiating .

we have g(x) = tan-1x

On differentiating 

Now the derivative of f(x) with respect to g(x) is

Hence the option (2) is correct.

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