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If y=(tanx)^(logx)+cos^2(pi/4) , find (d...

If `y=(tanx)^(logx)+cos^2(pi/4)` , find `(dy)/(dx)`

Text Solution

Verified by Experts

Given that,
`y=(tanx)^(logx)+cos^2(pi/4)`
Let `u=(tanx)^(logx)`
`=>log u= logx log(tanx)`
`=>1/u(du)/(dx)=1/x*log(tanx)+logx*1/tanx *sec^2x`
`=>(du)/(dx)=u[(log(tanx))/x+(logx*sec^2x)/tanx]`
`=>(du)/(dx)=(tanx)^(logx)[(log(tanx))/x+(logx*sec^2x)/tanx]`
so,`(dy)/(dx)=(tanx)^(logx)[(log(tanx))/x+(logx*sec^2x)/tanx]`
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