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

2 Answers
TheProteanGirl · Kalit Gautam
Apr 25, 2018

#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#

Jim G.
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#

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