TS EAMCET · Maths · Differentiation
If \(y=\frac{a x+b}{c x+d}\), than \(\frac{d x}{d y}=\)
- A \(\frac{a d-b c}{(a x+b)^2}\)
- B \(\frac{a d-b c}{(a-c y)^2}\)
- C \(\frac{a d+b c}{(c x+d)^2}\)
- D \(\frac{a d+b c}{(a+c y)^2}\)
Answer & Solution
Correct Answer
(B) \(\frac{a d-b c}{(a-c y)^2}\)
Step-by-step Solution
Detailed explanation
Given \(y=\frac{a x+b}{c x+d}\) \(\Rightarrow \mathrm{x}=\frac{\mathrm{b}-\mathrm{yd}}{\mathrm{yc}-\mathrm{a}}\) \(\text { now } \frac{\mathrm{dx}}{\mathrm{dy}}=\frac{\mathrm{ad}-\mathrm{bc}}{(\mathrm{yc}-\mathrm{a})^2}\)
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