using first principle find the derivative of f(x)=x-1/x+1

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Please find below the solution to the asked query:

We have:fx=x-1x+1fx+h=x+h-1x+h+1By first principle, we get:f'x=limh0 fx+h-fxh=x+h-1x+h+1-x-1x+1h=limh0x+h-1x+1-x+h+1x-1x+h+1x+1h=limh0x2+x+hx+h-x-1-x2-x+hx-h+x-1x+h+1x+1hlimh0x2+x+hx+h-x-1-x2+x-hx+h-x+1x+h+1x+1h=limh0h+hx+h+1x+1h=limh02hx+h+1x+1h=limh02x+h+1x+1Apply limitf'x=2x+0+1x+1f'x=2x+12

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