TS EAMCET · Maths · Differentiation
If \(\frac{d}{d x}\left\{\left(\frac{x-1}{x-\sqrt{x}}\right) e^{2 x+1}\right\}=\frac{x-1}{x-\sqrt{x}} e^{2 x+1} f(x)\), then \(f(4)=\)
- A \(0\)
- B \(1\)
- C \(\frac{35}{24}\)
- D \(\frac{47}{24}\)
Answer & Solution
Correct Answer
(D) \(\frac{47}{24}\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{d x}\left\{\left(\frac{x-1}{x-\sqrt{x}}\right) e^{2 x+1}\right\} = \frac{d}{d x}\left\{\left(\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}(\sqrt{x}-1)}\right) e^{2 x+1}\right\}\) \( = \frac{d}{d x}\left\{\left(1+x^{-1/2}\right) e^{2 x+1}\right\}\)…
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