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Question

If y=3x-13x+1sinx+loge1+x,x>-1, then at x=0, dydx is equal to


A

1

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B

0

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C

-1

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D

-2

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Solution

The correct option is A

1


Explanation for the correct option.

Find the value of dydx at x=0.

Differentiate the equation y=3x-13x+1sinx+loge1+x with respect to x.

dydx=ddx3x-13x+1sinx+loge1+x=3xlog33x+1-3x-13xlog33x+12sinx+3x-13x+1cosx+11+x

Now to find the value of dydx at x=0 substitute 0 for x.

dydxx=0=30log330+1-30-130log330+12sin0+30-130+1cos0+11+0=1×log3×1+1-1-1×1×log31+12×0+1-11+1×1+11=0+01+1=0+1=1

Thus at x=0, dydx=1.

Hence, the correct option is A.


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