COMEDK · Maths · 26. Differentiation
If \(f(x)=\dfrac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}\) then the value of \(f^{\prime}(0)\) is equal to
- A 11
- B 15
- C 13
- D 2
Answer & Solution
Correct Answer
(C) 13
Step-by-step Solution
Detailed explanation
Given \(f(x) = \dfrac{(x+1)^7 \sqrt{1+x^2}}{(x^2-x+1)^6}\). Taking the natural logarithm on both sides: \(\ln f(x) = 7 \ln(x+1) + \dfrac{1}{2} \ln(1+x^2) - 6 \ln(x^2-x+1)\). Differentiating both sides with respect to \(x\):…
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