How do you differentiate $y = 12 ln x$ $y=12lnx$ ?

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Answer 1 · 2018-04-10T06:34:18

The derivative of $12 ln x$ $12lnx$ is $\frac{12}{x}$ $12/x$ .

Using the fact that the derivative of $ln x$ $lnx$ is $\frac{1}{x}$ $1/x$ :

$= \frac{d}{d x} [12 ln x]$ $color(white)=d/dx[12lnx]$

$= 12 \cdot \frac{d}{d x} [ln x]$ $=12*d/dx[lnx]$

$= 12 \cdot \frac{1}{x}$ $=12*1/x$

$= \frac{12}{x}$ $=12/x$

Here's a short proof for the derivative of $ln x$ $lnx$ .

We know that $\frac{d}{d x} [x] = 1$ $d/dx[x]=1$ , that $\frac{d}{d x} [e^{x}] = e^{x}$ $d/dx[e^x]=e^x$ , also that $e^{ln x} = x$ $e^lnx=x$ :

$\frac{d}{d x} [x] = 1$ $d/dx[x]=1$

$\frac{d}{d x} [e^{ln x}] = 1$ $d/dx[e^lnx]=1$

$e^{ln x} \cdot \frac{d}{d x} [ln x] = 1$ $e^lnx*d/dx[lnx]=1$

$x \cdot \frac{d}{d x} [ln x] = 1$ $x*d/dx[lnx]=1$

$\frac{d}{d x} [ln x] = \frac{1}{x}$ $d/dx[lnx]=1/x$

How do you differentiate y=12lnxy=12lnxy=12lnx?