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Musical 'modes' are basically a set of tonalities deriving from a normal natural major scale. With C major, for example, it seems obvious that one should begin and end on C: C-D-E-F-G-A-B-C. But what if w...

Using the product rule we know that dy/dx = uv' + vu' where u = 3x^3; v = e^x. e^x differentiates to itself multiplied by any number in front of the x. u' = 9x^2; v' = e^x. Therefore dy/dx = 3x^3e...