Question

find the derivative of log(x) from first principle​

Answer 1

Answer:

Derivative of Log X

Let us suppose that the function is of the form y=f(x)=logax.

Dividing both sides by Δx, we get. ΔyΔx=1Δxloga(1+Δxx)

Consider Δxx=u⇒xΔx=1u, as Δx→0 then u→0, we get. ⇒dydx=1xlimu→0loga(1+u)1u.

Example: Find the derivative of y=f(x)=log10x2.

We have the given function as. ...

Differentiating with respect to variable x, we get.