TS EAMCET · Maths · Differentiation
If \(\log y=y^{\log \mathrm{x}}\) then \(\frac{d y}{d x}=\)
- A \(\frac{y(\log y)^2}{x(1-\log x \log y)}\)
- B \(\frac{x(\log x)^2}{y(1-\log x \log y)}\)
- C \(\frac{x(1-\log x \log y)}{y(\log y)^2}\)
- D \(\frac{y(1-\log x \log y)}{x(\log x)^2}\)
Answer & Solution
Correct Answer
(A) \(\frac{y(\log y)^2}{x(1-\log x \log y)}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { (a) } \log y=y^{\log x} \\ & \log (\log y)=\log x \cdot \log y \end{aligned}\) Differentiate both sides w.r.t. \(x\)…
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