AP EAMCET · Maths · Differentiation
If \(5 f(x)+3 f\left(\frac{1}{x}\right)=x+2\) and \(y=x f(x)\), then \(\frac{d y}{d x}\) at \(x=1\) is equal to
- A \(14\)
- B \(\frac{7}{8}\)
- C \(1\)
- D \(7\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{8}\)
Step-by-step Solution
Detailed explanation
At \(x=1\): \(5 f(1)+3 f\left(\frac{1}{1}\right)=1+2\) \(8 f(1)=3 \implies f(1)=\frac{3}{8}\) Differentiating the given equation: \(5 f'(x)+3 f'\left(\frac{1}{x}\right) \cdot \left(-\frac{1}{x^2}\right)=1\) At \(x=1\): \(5 f'(1)+3 f'(1) \cdot (-1)=1\)…
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