What is the derivative of ln(8x)?

3 Answers
Oct 16, 2015

1/x

Explanation:

Rule : d/dxlnu(x)=1/u*(du)/dx

therefore d/dx[ln(8x)]=1/(8x)*d/dx(8x)

=8/(8x)=1/x

Oct 16, 2015

1/x

Explanation:

The derivative of ln(nx) is equal to (((nx)')/(nx)) or the derivative of the inside of the natural log divided by the inside of the natural log.

The derivative of 8x is just 8, so it would be:

8/(8x) which is just 1/x

Hope this helped!

Oct 16, 2015

An alternative solution using the properties of logarithms.

Explanation:

Instead of using the chain rule, we can use the property of logarithms ln(ab) = lna+lnb to rewrite:

y = ln(8x) = ln8+lnx

Now, since ln8 is some constant, its derivative is 0, so we get"

dy/dx = 0+1/x=1/x