Differentiate the following function from first principles: `logcosx`

Explanation

We have given: `logcosx`

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

`implies f(x+h)=logcos(x+h)`

Hence,

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

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

`d/(dx)(f(x))=lim_(h->0)(log(1+(cos(x+h))/(cosx)-1))/h`

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