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)#