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Find (dy)/(dx) if, y=e^x+10^x+x^x...

Find `(dy)/(dx)` if, `y=e^x+10^x+x^x`

Text Solution

Verified by Experts

Given that,
`y=e^x+10^x+x^x`
Consider `t=x^x`
Taking log on both sides
`logt=xlogx`
Differentiating w.r.t. x, we get,
`=>1/t(dt)/(dx)=1+logx`
`=>(dt)/(dx)=t(1+logx)`
`=>(dt)/(dx)=x^x(1+logx)`
so,`(dy)/(dx)=d/(dx)e^x+10^x+x^x`
`=e^x+10^x log 10+x^x(1+logx)`
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