AP EAMCET · Maths · Differentiation
If g is the inverse of the function \(\mathrm{f}(\mathrm{x})\) and \(\mathrm{g}(\mathrm{x})=\mathrm{x}+\tan \mathrm{x}\) then, \(\mathrm{f}^{\prime}(\mathrm{x})=\)
- A \(1+\sec ^2 x\)
- B \(\frac{1}{1+\sec ^2 f(x)}\)
- C \(\frac{1}{1+\sec ^2 g(x)}\)
- D \(1+\sec ^2 f(x)\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{1+\sec ^2 f(x)}\)
Step-by-step Solution
Detailed explanation
\(g(x) = x + \tan x\) \(g'(x) = 1 + \sec^2 x\) \(f'(x) = \frac{1}{g'(f(x))}\) \(f'(x) = \frac{1}{1 + \sec^2 (f(x))}\)
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