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if y = tan^-1(2^x/(1+2^(2x+1))) then dy/...

if `y = tan^-1(2^x/(1+2^(2x+1)))` then `dy/dx at x =0` is

A

1

B

2

C

In 2

D

`-(1)/(10) In 2`

Text Solution

Verified by Experts

`y=tan^(-1)((2^(x+1)-2^(x))/(1+2^(x)cdot2^(x+1)))=tan^(-1)2^((x+1))-tan^(-1)2^(x)`
`therefore" "y'=(2^(x+1)In 2)/(1+(2^(x+1))^(2))-(2^(x)In2)/(1+(2^(x))^(2))`
`or "y'(0)=-(1)/(10)In 2`
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