# What is the second derivative of #f(x)= ln sqrt(x)#?

##### 2 Answers

Feb 28, 2016

The second derivative is

Note that

Feb 28, 2016

#### Explanation:

We can simplify

#log_a(b^c)=c*log_a(b)#

Here, we see that

#f(x)=lnsqrtx=ln(x^(1/2))=1/2ln(x)#

So, to find the derivative of this function, we must know that the derivative of

#f'(x)=1/2(1/x)#

To differentiate this and find the second derivative, use the **power rule**, recalling that

#f''(x)=1/2d/dx(x^-1)=1/2(-x^-2)=-1/(2x^2)#