compound trig function

[red and white kop!]

differentiate wrtx the function ln(cosx)
i found -(sinxcosx)/x but the right answer is -tanx
why is this?

 

[daon]

If u is a function of x, then D[ln(u)] = 1/u*du/dx. It really is just the chain rule, but I see that it is often singled out and written "u'/u".

 

[Deleted member 4993]

differentiate wrtx the function ln(cosx)
i found -(sinxcosx)/x but the right answer is -tanx
why is this?

\(\displaystyle \frac{d}{dx} ln[cos(x)] = \frac{1}{cos(x)} \cdot \frac{d}{dx}[cos(x)] = \frac{1}{cos(x)} \cdot [-sin(x)] = - tan(x)\)

 

[red and white kop!]

thanks