How do you differentiate $f(x)= ln(2x+1)^(-1/2)$ ?

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Answer 1 · 2017-11-16T00:44:00

$=1/((2x+1)sqrt(ln(2x+1)))$

$d/dx sqrt(ln(2x+1)) = 1/(2sqrt(ln(2x+1)))*d/dxln(2x+1)$

$= 1/(2sqrt(ln(2x+1)))*1/(2x+1) *d/dx (2x+1)$

$=1/(cancel(2)sqrt(ln(2x+1)))*1/(2x+1) *cancel(2)$

$=1/((2x+1)sqrt(ln(2x+1)))$

Basically, it is the chain rule a bunch of times.

I hope that helps!

How do you differentiate f(x)= ln(2x+1)^(-1/2) f(x)= ln(2x+1)^(-1/2) ?