Question

Derivative of [arcsec(u)/3u+2]

Answer 1

Quotient rule

Answer 2

\[\huge y'=\frac{(3u+2)(\frac{1}{\sqrt{1-\frac{1}{u^2}} u^2})-3\sec^{-1}u}{(3u+2)^2}\]

Multiply top and bottom by

\[\frac{1}{\sqrt{1-\frac{1}{u^2}} u^2}\]

Answer 3

Would the answer be [(3u+2)/(u^2-1)^(1/2)] for the top first part?

Answer 4

yes \[\huge \frac{\frac{3 u+2}{\sqrt{1-\frac{1}{u^2}} u^2}-3 \sec ^{-1}(u)}{(3 u+2)^2}\]