1.

\text { If } y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \ldots .\left(1+x^{2 n}\right) \text { then the value of }\left(\frac{d y}{d x}\right) \text { at } x=0 \text { is }\(\text { If } y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \ldots .\left(1+x^{2 n}\right) \text { then the value of }\left(\frac{d y}{d x}\right) \text { at } x=0 \text { is }\)

Answer»

y=(1+x)(1+x2)(1+x4)......(1+x2n)

⇒log y =Iog (1+x)+ Iog (1+x2) ......+ Iog (1+x2n)
⇒1/y. dy/dx= 1/(1+x )+ 2x/(1+x2 )......+ 2nx2n−1/(1+x2n)

⇒dy/dx= y.(1/1+x + 2x/1+x2.......+ 2nx2n−1/1+x2n)
Substitute the value x=0,
⇒∣dy/dx∣x=0 =1.1 = 1


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