Question 1033387
{{{ dtanhx / dx = d(sinhx/coshx) / dx   = ((dsinhx/dx)*cosh - sinhx*(dcoshx/ dx))/cosh^2(x) }}}  by direct application of the quotient rule...

= {{{(coshx*coshx - sinhx*sinhx)/cosh^2(x) = (cosh^2(x) - sinh^2(x))/cosh^2(x) = 1/cosh^2(x) = sech^2(x)}}}