# How do you find the first and second derivative of #ln(x/2)#?

##### 1 Answer

Nov 12, 2016

#### Answer:

# dy/dx= 1/x#

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

#### Explanation:

Let

We can use the law of logarithms to write:

# y= lnx - ln2 #

Differentiating wrt

# dy/dx= 1/x#

We can rewrite this as:

# dy/dx= x^-1 #

Differentiating again wrt

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

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