AP EAMCET · Maths · Differentiation
Express \(\frac{d t}{d x}=\frac{t}{\left(x+t e^{-2 x / 4}\right)}\) in the form of \(\frac{d x}{d t}=\phi\left(\frac{x}{t}\right)\)
- A \(\frac{x}{t}+e^{-2\left(\frac{x}{t}\right)}\)
- B \(\frac{x}{t}-e^{-2\left(\frac{x}{t}\right)}\)
- C \(\frac{x}{t}+e^{2\left(\frac{x}{t}\right)}\)
- D \(\frac{x}{t}-e^{2\left(\frac{x}{t}\right)}\)
Answer & Solution
Correct Answer
(A) \(\frac{x}{t}+e^{-2\left(\frac{x}{t}\right)}\)
Step-by-step Solution
Detailed explanation
\(\frac{d t}{d x}=\frac{t}{x+t e^{\frac{-2 x}{t}}}\) On reciprocal, we get \[ \frac{d x}{d t}=\frac{x+t e^{\frac{-2 x}{t}}}{t}=\left(\frac{x}{t}\right)+e^{-2\left(\frac{x}{t}\right)} \] Hence, option (1) is correct.
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