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Find the derivative of f from the first ...

Find the derivative of f from the first principles, where f is given by(i) `f(x)=(2x+3)/(x-2)` (ii) `f(x)=1/x`

Text Solution

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we know that `f'(x)=lim_(h->0)(f(x+h)-f(x))/h`
Given `f(x)=(2x+3)/(x-2)`
`f(x+h)=(2(x+h)+3)/((x+h)-2)=(2x+3+2h)/(x-2+h)`
Now, `f'(x)=lim_(h->0)((2x+3+2h)/(x-2+h)-(2x+3)/(x-2))/h`
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