find the derivative of ln 2.21/12 ln(1+0.0833r) using quotient rule

Question

i need help finding the derivative.

Answer 1

ln(2.21)/(12 * ln(1+0.0833r) )

f(x) = g(x)/h(x)

f ' (x) = (g'(x)h(x) - g(x)h'(x)) / (h(x))^2

(0 - ln(2.21)( 12 * (1/(1+0.0833r)) * (0.0833) ) ) / (12 * ln(1+0.0833r))^2

-12/0.0833 * ln(2.21) * (1/(1+0.0833r)) / (144)(ln(1+0.0833r))^2

-1/(12*0.0833) * ln(2.21) * (1/(1+0.0833r)) / (ln(1+0.0833r))^2

-ln(2.21)/(12*0.0833) * (1/(1+0.0833r)) / (ln(1+0.0833r))^2

Note:  The bit on the bottom is (ln(1+0.0833r))^2 not ln( (1+0.0833r)^2 ), so it doesn't simplify to 2ln(1+0.0833r).

-ln(2.21) / (0.9996 * (1+0.0833r) * ( ln(1+0.0833r) )^2 )

That should be it.  Not sure how to reduce it any further.

Comments

thanks a lot. that helped big time. thumbs up.

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You're welcome.  We aim to please.