TS EAMCET · Maths · Differentiation
If \(f(x)=\frac{1}{x^3} \int_5^x\left(2 u^2-u f^{\prime}(u) d u\right.\), then \(f^{\prime}(5)=\)
- A \(\frac{13}{2}\)
- B \(\frac{2}{13}\)
- C \(\frac{13}{5}\)
- D \(\frac{5}{13}\)
Answer & Solution
Correct Answer
(D) \(\frac{5}{13}\)
Step-by-step Solution
Detailed explanation
Given, \(\begin{aligned} f(x) & =\frac{1}{x^3} \int_5^x\left(2 u^2-u f^{\prime}(u) d u\right. \\ \Rightarrow \quad x^3 f(x) & =\int_5^x\left(2 u^2-u f^{\prime}(u)\right) d u \end{aligned}\) On differentiating w.r.t ' \(x\) ',…
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