Find the derivative of the function given by f (x) = (1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) and hence find f ′(1).

Question

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

Philoid · Accepted Answer

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

Taking log on both sides, we get

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

Now, differentiate both sides with respect to x

Find the derivative of the function given by f (x) = (1 + x) (1 + x2) (1 + x4) (1 + x8) and hence find f ′(1).