use logarithmic differentation to find dydx if ycoshx2xSolut

Solution

Given
y=(coshx)^(2x)
Then
log(y)=log((coshx)^(2x))
Remember that log(A^B)=B*log(A), thus
log(y)=2xlog(coshx)
Then, differentiating
y\'/y=2log(coshx)+2x(sinhx/coshx)=2log(coshx)+2xtanhx
Hence
y\'=((coshx)^(2x))(2log(coshx)+2xtanhx)