Question

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

Answer 1

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

Explanation:

`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!