AP EAMCET · Maths · Differentiation
\(\frac{d}{d x} \frac{(x+1)^2 \sqrt{x-1}}{(x+4)^3 e^x}=f(x)\left[\begin{array}{c}\frac{2}{x+1}+\frac{1}{2(x-1)} \\ -\frac{3}{x+4}-1\end{array}\right]\)then \(f(5)=\)
- A \(\frac{72}{81} e^5\)
- B \(\frac{7}{81 e^5}\)
- C \(\frac{8}{81 e^5}\)
- D \(e^5\)
Answer & Solution
Correct Answer
(C) \(\frac{8}{81 e^5}\)
Step-by-step Solution
Detailed explanation
Let \(y=f(x)=\frac{(x+1)^2 \sqrt{x-1}}{(x+4)^3 e^x}\) \(\begin{aligned} & \Rightarrow \log y=\log \left[\frac{(x+1)^2 \sqrt{x-1}}{(x+4)^3 e^x}\right] \\ & \Rightarrow \quad \log y=2 \log (x+1)+\frac{1}{2} \log (x-1)\end{aligned}\) \(-3 \log (x+4)-x\) On differentiating both…
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