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Question

If 2x+2y=2x+y, then dydx is equal to


A

(2x+2y)(2x2y)

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B

(2x+2y)(1+2x+y)

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C

2x-y(2y-1)(12x)

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D

None of these

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Solution

The correct option is C

2x-y(2y-1)(12x)


Explanation for the correct option:

Step 1. Find the value of dydx:

Given, 2x+2y=2x+y

2x+2y=2x2y

Step 2. Differentiate it with respect to x

2xlog2+2ylog2dydx=2x2ylog2dydx+2y2xlog2

dydx(2ylog22x2ylog2)=2y2xlog22xlog2

dydx2ylog2(12x)=2xlog2(2y-1)

dydx=2xlog2(2y-1)2ylog2(12x)=2x(2y-1)2y(12x)=2x-y(2y-1)(12x)

Hence, Option ‘C’ is Correct.


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