Richie Sambora Offers Free Guitar Lessons to Anna Nicole Smith's Daughter Dannielynn

Anna Nicole Smith's daughter, Dannielynn Birkhead, may be too young to know how to pull strings, but she'll now be able to play them thanks to none other than Richie Sambora!

Her dad, Larry Birkhead, tells TMZ ... this weekend's Kentucky Derby was insanely momentous for his 15-year-old daughter ... as we reported, she wore the same getup that Janet Jackson wore to the Derby in years past, and even met Janet this time around.

But that wasn't the end of it. Sambora performed at the Barnstable Brown Gala during Derby weekend -- the same place Anna Nicole Smith and Larry Birkhead met in 2003.

Dannielynn was front and center and even brought her own guitar to the event, hoping to get a John Hancock from Richie. She got way more than she bargained for, because the next day she ran into Richie and he offered her lessons to master the instrument!

Here's the catch. Larry and Dannielynn live in Kentucky, and Richie is ensconced in L.A., so the rocker said anytime she makes it out to La La Land, he'll be there for her.

Richie gave her words of encouragement, urging her to follow her dreams of being an accomplished guitarist. Larry says it was so overwhelming, his daughter almost fainted.

Richie told them he doesn't usually offer lessons but he made a special exception for Dannielynn.