Question

if Y =(1+x) (1+x^2) (1+x^4) (1+x^8) then find f '(x) at x=1​

Answer 1

$\huge\underline\bold {Answer:-}$

Let y = (1 + x)(1 + x^2)( 1+ x^4)(1+x^8)

Taking log both sides we get,

$log(y) = (1 + x)(1 + x {}^{2} )(1 + x {}^{4} (1 + x {}^{8} )$

Since,

$log(ab) = log(a) + log(b)$

$= > log(y) = log(1 + x ) log (1 + x {}^{2} ) log (1 + x {}^{4} ) log(1 + x {}^{8})$

For more explanation..please refer to the attachment.

Hence your final answer is 120.