If y=e^(ax)cos^3 x sin^2 x find dy/dx

it's a differential equation.
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11 Answers

Let F_=e^ax,
by Level 12 User (101k points)
G_=COS^3x
by Level 12 User (101k points)
& H_=SIN^2x :
by Level 12 User (101k points)
Y'==(F•G•H)'
by Level 12 User (101k points)
=[F•(G•H)']
by Level 12 User (101k points)
=F'•(GH)+F•(GH)'
by Level 12 User (101k points)
→ Y'=F'GH+FG'H+FGH'
by Level 12 User (101k points)
F'=ae^ax,
by Level 12 User (101k points)
G'=-3SINX•COS^2X ,
by Level 12 User (101k points)
H'=2SINX•COSX
by Level 12 User (101k points)
Therefore: Y'=e^ax•SINX•COS^2X•(a SINX•COSX-3SIN^2X+2COS^2X)
by Level 12 User (101k points)

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