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"If "y=(1+x)(1+x^(2))(1+x^(4))...(1+x^(2...

`"If "y=(1+x)(1+x^(2))(1+x^(4))...(1+x^(2^(n)))," then find "(dy)/(dx)at x= 0.`

A

1

B

-1

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`y=(1+x)(1+x^(2))(1+x^(4))….(1+x^(2^(n)))`
`implies" "y=((1-x)(1+x)(1+x^(2))(1+x^(4))….(1+x^(2^(n))))/((1-x))`
`implies" "y=(1-x^(2^(n+1)))/(1-x)`
`implies" "(dy)/(dx)=(-2^(n+1)x^(2^(n+1)-1)"("1-x")"+"("1-x^(2^(n+1))")")/((1-x)^(2))`
`implies" "((dy)/(dx))_(x=0)=1`
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OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Section I - Solved Mcqs
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  7. If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0...

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  12. If y=sin^(-1)(sin x), then dy/dx at x =pi/2 is

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  13. "If "y=sec (tan^(-1)x)," then "(dy)/(dx)" at "x=1 is equal to

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  14. Let f be a differentiable function satisfying [f(x)]^(n)=f(nx) for all...

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