What is the derivative of $log_3x$ ?

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Answer 1 · 2018-03-31T20:40:01

$d/dx(log_3x)=1/(xln3)$

We can rewrite $log_3x$ as $ln(x)/ln(3)$ .

So, we really want $d/dx(lnx)/ln3$ . Knowing that $d/dxlnx=1/x$ , we get

$d/dx(lnx)/ln3=1/(xln3)$ .

This gives rise to the general differentiation rule

$d/dxlog_ax=1/(xlna).$

Answer 2 · 2018-03-31T21:14:02

$d/dx[log_3(x)]=1/(ln(3)*x)$

There is a rule here:

$d/dx[log_a(x)]=1/((ln(a)*x))*d/dx[x]$

Therefore:

$d/dx[log_3(x)]=1/(ln(3)*x)*d/dx[x]$

The derivative of $x$ is just $1$ . Therefore:

$d/dx[log_3(x)]=1/(ln(3)*x)$

What is the derivative of log_3xlog_3x?