What is the second derivative of f(x)=ln (x+3)?

2 Answers

f''(x) = -1/(x+3)^2

Explanation:

NOTE that the Derivative of ln(x) = 1/x and derivative of 1/x = -1/x^2

f'(x)=(d{ln(x+3)})/dx =1/(x+3)

f''(x) = (d{1/(x+3)})/dx = -1/(x+3)^2

Apr 25, 2018

f''(x)=-1/(x+3)^2

Explanation:

"differentiate using the "color(blue)"chain rule"

"Given "y=f(g(x))" then"

dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"

rArrf'(x)=1/(x+3)xxd/dx(x+3)=1/(x+3)=(x+3)^-1

"differentiate "f'(x)" using the chain rule"

rArrf''(x)=-(x+3)^-2xxd/dx(x+3)=-1/(x+3)^2