Answer:
[tex]f''(x)=-\frac{2}{x^2}[/tex]
Step-by-step explanation:
We are given that
[tex]f(x)=3+2lnx[/tex]
We have to find the second order of given function
To find the highest order derivative using the formula given below
[tex]\frac{d^nA}{dx^n}=\frac{d(\frac{d^{n-1}A}{dx^{n-1}})}{dx}[/tex]
Differentiate w.r.t.x
[tex]f'(x)=2\frac{1}{x}=\frac{2}{x}=2x^{-1}[/tex]
By using the formula [tex]\frac{d(lnx)}{dx}=\frac{1}{x}[/tex]
[tex]\frac{1}{x}=x^{-1}[/tex]
Substitute n=2
[tex]f''(x)=\frac{d^2f(x)}{dx^2}=\frac{d(f'(x))}{dx}=-2x^{-2}=-\frac{2}{x^2}[/tex]
By using the formula
[tex]\frac{d(x^n)}{dx}=nx^{n-1}[/tex]
Hence, the second order derivative of function is given by
[tex]f''(x)=-\frac{2}{x^2}[/tex]
