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

Explanation

We have given: `e^(sqrt(2x))`

Let `y=f(x)=e^(sqrt(2x))`br>
Now differentiating w.r.to `x` by using first principle we get

`implies f(x+h)=e^(sqrt(2(x+h)))`

Hence,

`d/(dx)(f(x))=lim_(h->0)(f(x+h)-f(x))/h`

`d/(dx)(f(x))=lim_(h->0)(e^(sqrt(2(x+h)))-e^(sqrt(2x)))/h`

`d/(dx)(f(x))=lim_(h->0) (e^(sqrt2x)(e^(sqrt(2(x+h))-sqrt(2x))-1))/h`

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