Differentiate the following function from first principles: `e^(sqrt(2x))`

Explanation

We will differentiate the given function using first priciple.

Here, `f(x) = e^sqrt(2x)`

`:. f'(x) = Lim_(h->0) (f(x+h) - f(x))/h`

`= Lim_(h->0) (e^sqrt(2(x+h)) - e^sqrt(2x))/h`


`= e^sqrt(2x) Lim_(h->0) (e^(sqrt(2(x+h)) - sqrt(2x)) -1)/h`

`= e^sqrt(2x) Lim_(h->0) (e^(sqrt(2(x+h)) - sqrt(2x))-1)/h**(sqrt(2(x+h)) - sqrt(2x))/(sqrt(2(x+h)) - sqrt(2x))`


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