Differentiate the following function from first principles: `e^(a x+b)`

Explanation

We have given: `e^(ax+b)`

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

`implies f(x+h)=e^(a(x+h)+b)`

Hence,

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

`d/(dx)(f(x))=lim_(h->0)(e^(a(x+h)+b)-e^(ax+b))/h`

`d/(dx)(f(x))=lim_(h->0) (e^(ax+b)(e^(ah)-1)a)/(ah)`

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