AP EAMCET · Maths · Differentiation
If \(y=\log _y x\), then \(\frac{d y}{d x}\) is equal to
- A \(\frac{1}{x \log y}\)
- B \(\frac{\log y}{x(1+\log y)}\)
- C \(\frac{1}{x(1+\log y)}\)
- D \(\frac{1}{1+\log y}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{x(1+\log y)}\)
Step-by-step Solution
Detailed explanation
\(\because y=\log _y x\) To find, \(\frac{d y}{d x}\) \(\Rightarrow \quad y=\frac{\log _e x}{\log _e y}\) \(y \log y=\log x\) On differentiating w.r.t. \(x\), \(y \cdot \frac{d}{d x} \log y+\log y \cdot \frac{d y}{d x}=\frac{d}{d x} \log x\)…
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