To derive the melodic minor scale we raise the ♭6 of the harmonic minor scale one half step to a major 6. Raising the 6th degree of the scale smoothes out the awkward augmented 2nd of the harmonic minor scale. Here is the A melodic minor scale:

R 2 ♭3 4 5 6 7 R
A B C D E F# G# A

The melodic minor scale can also be understood as a major scale with a flatted 3rd. Thinking of it this way makes it really easy to see on your guitar, if you already know your major scales.

In classical music the melodic minor is played ascending, but the descending melodic minor scale is the same as the natural minor scale.

Sometimes the melodic minor is called the jazz minor. In jazz the descending melodic minor is the same as the ascending form; it is not the same as the natural minor scale. The jazz minor and the modes (other scales derived from it – this concept is discussed in the next section) of the melodic minor scale are extremely common in jazz.

Here are the CAGED Guitar patterns of the G Minor Melodic Scale:
The Melodic Minor Scale

You may be wondering if you can use any of these scales (Harmonic Minor, Melodic Minor) in the blues. The answer is yes! Later on I will show you how, so stick with me!