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Question

If y=1+x1+x21+x4, then dydx at x=1 is


A

20

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B

28

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C

1

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D

0

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Solution

The correct option is B

28


Explanation for the correct option.

Step 1. Differentiate y with respect to x.

Given an equation y=1+x1+x21+x4. Now using the product rule of differentiation, differentiate both sides with respect to x.

dydx=ddx1+x1+x21+x4=1·1+x21+x4+1+x·2x·1+x4+1+x1+x2·4x3=1+x21+x4+2x1+x1+x4+4x31+x1+x2

Step 2. Find the value of dydx at x=1

In the expression 1+x21+x4+2x1+x1+x4+4x31+x1+x2 substitute x=1.

dydxx=1=1+121+14+2×11+11+14+4×131+11+12=2×2+2×2×2+4×2×2=4+8+16=28

Hence, the correct option is B.


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