JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(g \) is the inverse of a function \(f \) and \(f'\left( x \right) = \frac{1}{{1 + {x^5}}}\) thne \(g'\left( x \right)\) is equal to :
- A \(\frac{1}{{1 + {{(g\left( x \right))}^5}}}\)
- B \(1 + {(g\left( x \right))^5}\)
- C \(1 + {x^5}\)
- D \(\;5{x^4}\)
Answer & Solution
Correct Answer
(B) \(1 + {(g\left( x \right))^5}\)
Step-by-step Solution
Detailed explanation
\(f(g(x))=x\) \(f^{\prime}(g(x)) g^{\prime}(x)=1\) \(g^{\prime}(x)=\frac{1}{f^{\prime}(g(x))}\) \(g^{\prime}(x)=\frac{1}{\frac{1}{1+(g(x))^{5}}}\) \(1+(g(x))^{5}\)
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