# Math Help - simplify log derivative/distribution

1. ## simplify log derivative/distribution

I have been having trouble trying to follow along an example of, finding the derivative of $(11x)^{ln11x}$ .

Using the property $A^r = rlnA$

$ln(f(x))= (ln11x) (ln11x)$

Now differentiate the left side, then the right side....

Left Side: $\frac{d}{dx}[ln(f(x))]= \frac{1}{f(x)}f'(x)$

Right side: $\frac{d}{x}[(ln11x) (ln11x)] = \frac{2ln11x}{x}$

$\frac{1}{f(x)}f'(x) = \frac{2ln11x}{x}$

multiply both sides by f(x) , to get f'(x) by itself. $f'(x) = f(x)* \frac{2ln11x}{x}$

Now replcace f(x) for $(11x)^{ln11x}$

$f'(x) = (11x)^{ln11x} * \frac{2ln11x}{x}$

I getting confused at this part...... how does it get to here

$= 2* 11^{ln11x}x^{ln11x-1}ln11x$

2. ## Re: simplify log derivative/distribution

$(11x)^{ln11x} = 11^{ln11x}x^{ln11x}$

So

$\frac{(11x)^{ln11x}}x= \frac{11^{ln11x}x^{ln11x}}x= 11^{ln11x}x^{ln11x-1}$

Now multiply both sides by $2ln11x$ and you are there.