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Find (dy)/(dx), when: y=(1+x)(1+x^(2))...

Find `(dy)/(dx),` when:
`y=(1+x)(1+x^(2))(1+x^(4))(1+x^(6))`

Text Solution

Verified by Experts

The correct Answer is:
`(1+x)(1+x^(2))(1+x^(4))(1+x^(6)).{(1)/((1+x))+(2x)/((1+x^(2)))+(4x^(3))/((1+x^(4)))+(6x^(5))/((1+x^(6)))}`
`logy=log(1+x)+log(1+x^(2))+log(1+x^(4))+log(1+x^(6))`
`rArr(1)/(y).(dy)/(dx)={(1)/((1+x))+(2x)/((1+x^(2)))+(4x^(3))/((1+x^(4)))+(6x^(5))/((1+x^(6)))}.`
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