21-47 Differentiate. y=ln(cosh3x)

To differentiate: y=lncos⁡h3x

Answer: y'=3tan⁡h3x

Given y=lncos⁡h3x

Differentiate w.r.t x

dydx=ddxlncos⁡h3x=1cos⁡h3x.ddxcos⁡h3x

y'=1cos⁡h3x.sin⁡h3x.3

⇒y'=3tan⁡h3x

Formula used:

ddxcos⁡hax=asin⁡hax

Conclusion:

y'=3tan⁡h3x