This is Emma Caroline Bootle Wilbraham who married Edward Geoffrey Smith Stanley, 14th Earl of Derby, in 1825. Her article in thepeerage is here.
From Paul Frecker; sepia tone removed (and re-added only to border with Photoshop) by gogm.
An older Countess Emma wears a crinoline, lace wrap, and a poke bonnet in this 1861 Silvy photo.
Keywords: 1861, Silvy, Bootle Wilbraham family, Smith Stanley family, Countess, floral bonnet, bows, high neckline, long flared sleeves, crinoline, lace shawl, wrap