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TS EAMCET · Maths · Differentiation

If \(2^x+2^y=2^{x+y}\), then \(\frac{d y}{d x}=\)

  1. A \(1-2^y\)
  2. B \(1-2^{-y}\)
  3. C \(1+2^y\)
  4. D \(1+2^{-y}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(1-2^y\)

Step-by-step Solution

Detailed explanation

It is given that, \(2^x+2^y=2^{x+y} \Rightarrow 2^{-y}+2^{-x}=1\) On differentiating both sides w.r.t. ' \(x\) ', we get \(\Rightarrow\left(-2^{-y} \frac{d y}{d x}-2^{-x}\right) \log 2=0\)…