Question

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

Answer 1

f(x)=(x+1)(x^2+1)(x^4+1)(x^8+1)

=(x^3+x+x^2+1)(x^12+x^4+x^8+1)

=×^15 + ×^7 + ×^11 + ×^3 + ×^13 + ×^5 + ×^9 + ×+×^14+×^6+×^10+×^2+×^12+×^4+×^8+1

f(1)=1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

=15

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