Question

find the nth derivative of log 3x​

Answer 1

❤Hey mate❤

d(log3x)/dx = 3/3x=**1/x** and d(log4x)/dx = 1*4/4x = **1/x **. Therefore the derivative of log3x and log4x is **1/x**

❤Hope this will helpful for you❤

Answer 2

The nth derivative of log 3x is $(x)^-^n.$

Given :

log 3x

To find:

The nth derivative of log 3x.

Solution:

The nth derivative of log(3x) can be found using the chain rule and the derivative of the natural logarithm function.

The first derivative of log(3x) is:

$d/dx log(3x) = 1/(3x) * d/dx (3x) \\d/dx log(3x) = 1/(3x) * 3 \\d/dx log(3x) = 1/x$

The nth derivative of log(3x) can be found by differentiating the previous result n-1 times:

$d^n/dx^n log(3x) = (-1)^(n-1) * (n-1)! / x^n$

$d^n/dx^n log(3x) = (x)^-^n$

So, the nth derivative of log(3x) is a function of x with a power of -n.

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