Question

Find the derivative of log x by ab- initio method



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Answer 1

Answer:

Log*by ab- initio is what you know just you write it

Answer 2

Find the derivative of log x by ab- initio method is 1/x

Explanation:

The differentiation of $log_{x}$ by ab-initio method

$y=log_{x}$

$y+$Δ$y=log(x+$Δ$x)$

$x$ is independent variable

Δ$y=log(x+$Δ$x)-y$

Δ$y=log(x+$Δ$x)-logx$

Δ$y=logx+$Δ$x/x$

Δ$y=log(1+$Δ$x/x)$

Δ$y/$Δ$x$$=log(1+$Δ$x/x)/$Δ$x$

$\frac{dy}{dx} = \lim_{Δ \to \ 0$

Δ$y/$Δ$x$$= \lim_{Δ \to \ 0$ $log(1+$Δ$x$Δ$x$

$\frac{dy}{dx} = \lim_{Δ\to \ 0$$log(1+$Δ$x/x)/$Δ$x/x$

$\frac{dy}{dx} = \lim_{Δ\to \ 0$$log(1+$Δ$x/x)/$Δ$x/x$ . $\frac{1}{x}$

∵ $\lim_{Δ\to \ 0$$log(1+$Δ $x/x)/$Δ  $x/x$$=1$

$=1*\frac{1}{x}$

$=\frac{1}{x}$  the derivative of log x by ab- initio method.