# Natural Derivative

• December 14th 2009, 11:09 AM
av8or91
Natural Derivative
f(x)= ln(5x^4-x)
• December 14th 2009, 11:17 AM
e^(i*pi)
Quote:

Originally Posted by av8or91
f(x)= ln(5x^4-x)

Use the chain rule

$\frac{d}{dx}ln[f(x)] = \frac{f'(x)}{f(x)}$

In your case $f(x)=5x^4-x$ which s pretty simple to differentiate
• December 14th 2009, 11:17 AM
Plato
Quote:

Originally Posted by av8or91
f(x)= ln(5x^4-x)

The derivative of $y=\ln(f(x))$ is $y'=\frac{f'(x)}{f(x)}$.

So what do you think?
• December 14th 2009, 11:21 AM
av8or91
oh ok I see it now I think. So its just the derivative of the top/ original function on the bottom.

20x^3-1
5x^4-x
• December 14th 2009, 11:27 AM
e^(i*pi)
Quote:

Originally Posted by av8or91
oh ok I see it now I think. So its just the derivative of the top/ original function on the bottom.

20x^3-1
5x^4-x

Aside from the syntax then yes

$\frac{20x^3-1}{5x^4-x}$