TS EAMCET · Maths · Differentiation
If \(f(x)=\log _{\left(x^2-2 x+1\right)}\left(x^2-3 x+2\right), x \in \mathbb{R}-[1,2]\) and \(x \neq 0\), then \(f^{\prime}(3)=\)
- A \(1\)
- B \(0\)
- C \(\log _e 4\)
- D \(\log _4 e\)
Answer & Solution
Correct Answer
(D) \(\log _4 e\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{\ln(x^2-3x+2)}{\ln(x^2-2x+1)} = \frac{\ln((x-1)(x-2))}{\ln((x-1)^2)} = \frac{\ln(x-1)+\ln(x-2)}{2\ln(x-1)} = \frac{1}{2} + \frac{\ln(x-2)}{2\ln(x-1)}\) \(f'(x) = \frac{1}{2} \left(\frac{\frac{1}{x-2}\ln(x-1) - \frac{1}{x-1}\ln(x-2)}{(\ln(x-1))^2}\right)\)…
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