TS EAMCET · Maths · Differentiation
If \(\mathrm{x}=\log \mathrm{p}\) and \(\mathrm{y}=\frac{1}{p}\) then \(\frac{d y}{d x}=\)
- A \(-\mathrm{e}^{-\mathrm{x}}\)
- B \(\mathrm{e}^{\mathrm{x}}\)
- C X
- D \(\mathrm{y}\)
Answer & Solution
Correct Answer
(A) \(-\mathrm{e}^{-\mathrm{x}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & x=\log p, y=\frac{1}{p} \\ \Rightarrow \quad & \frac{d y}{d p}=\frac{-1}{p^2} \Rightarrow \frac{d x}{d p}=\frac{1}{p} \\ \Rightarrow \quad & \frac{d y}{d x}=\frac{d y / d p}{d x / d p}=\frac{-1}{p^2} \times p=\frac{-1}{p} \\ \because \quad & x=\log p…
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