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Differentiate (1+cosx)^x with respect to...

Differentiate `(1+cosx)^x` with respect to `x` :

Text Solution

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Let y=`(1+cosx)^(x)`
log y=`log(1+cosx)^(x)`
`=xlog(1+cosx)`
Differentiate both sides with respect to x.
`(1/y)(dy)/(dx)=xcdotd/(dx)log(1+cosx)+log(1+cosx)cdotd/(dx)x`
`rArr(dy)/(dx)=y[x/(1+cosx)cdotd/(dx)(1+cosx)+log(1+cosx)]`
`rArr(dy)/(dx)=(1+cosx)^(x)[(-xsinx)/(1+cosx)+log(1+cosx)]`
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