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If y=[x+sqrt(x^2+a^2)]^n then prove that...

If `y=[x+sqrt(x^2+a^2)]^n` then prove that `(dy)/dx=(ny)/sqrt(x^2+a^2)`

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`y= [x+ sqrt(x^2 + a^2)]^n`
`dy/dx = n(x+ sqrt(x^2 + a^2))^(n-1) (1 + (2x)/(2sqrt(x^2+a^2)))`
`= n(x+ sqrt(x^2 + a^2))^(n-1) ((sqrt(a^2+x^2) + x)/(sqrt(a^2+x^2)))`
`= (n(x+ sqrt(a^2+x^2))^n)/(sqrt(a^2+x^2))`
`= (ny)/sqrt(a^2+x^2)`
Answer
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