Find the derivative of the function f(x) given by f(x) = (1 + x)(1 + x 2 )(1 + x 4 )(1 + x 8 ) and hence find f’(1)

Question

Philoid · Accepted Answer

Here,

f(x) = (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)

f(1) = (2)(2)(2)(2) = 16

Taking log on both sides we get,

Log (f (x)) = log (1 + x) + log (1 + x²) + log (1 + x⁴) + log(1 + x⁸)

Differentiating it with respect to x we get,

F’(1) = 120