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

it's a differential equation.
asked May 31, 2013

 Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: To avoid this verification in future, please log in or register.

Let F_=e^ax,
answered Jan 24 by Top Rated User (76,240 points)
G_=COS^3x
answered Jan 24 by Top Rated User (76,240 points)
& H_=SIN^2x :
answered Jan 24 by Top Rated User (76,240 points)
Y'==(F•G•H)'
answered Jan 24 by Top Rated User (76,240 points)
=[F•(G•H)']
answered Jan 24 by Top Rated User (76,240 points)
=F'•(GH)+F•(GH)'
answered Jan 24 by Top Rated User (76,240 points)
→ Y'=F'GH+FG'H+FGH'
answered Jan 24 by Top Rated User (76,240 points)
F'=ae^ax,
answered Jan 24 by Top Rated User (76,240 points)
G'=-3SINX•COS^2X ,
answered Jan 24 by Top Rated User (76,240 points)
H'=2SINX•COSX
answered Jan 24 by Top Rated User (76,240 points)
Therefore: Y'=e^ax•SINX•COS^2X•(a SINX•COSX-3SIN^2X+2COS^2X)
answered Jan 24 by Top Rated User (76,240 points)

## Related questions

13 answers 36 views
36 views
1 answer 264 views
264 views
0 answers 13 views
13 views
1 answer 169 views
169 views
9 answers 25 views
25 views
8 answers 161 views
161 views
25 answers 93 views
93 views
44 answers 35 views
35 views
0 answers 68 views
68 views
0 answers 21 views
21 views
1 answer 26 views
26 views
2 answers 155 views
155 views
1 answer 36 views
36 views
1 answer 227 views
227 views
20 answers 65 views
65 views
0 answers 77 views
77 views
1 answer 15 views
15 views
0 answers 15 views
15 views
53 answers 62 views
62 views
39 answers 110 views
110 views
34 answers 120 views
120 views
0 answers 40 views
40 views
0 answers 36 views
36 views
0 answers 45 views
45 views
45 answers 207 views
207 views
16 answers 118 views
118 views
20 answers 159 views
159 views
0 answers 99 views
99 views
38 answers 90 views
90 views
0 answers 28 views
28 views
1 answer 26 views
26 views
0 answers 42 views
42 views
1 answer 41 views
41 views
15 answers 20 views
20 views
8 answers 22 views
22 views
0 answers 16 views
16 views
0 answers 47 views
47 views
10 answers 74 views
74 views
8 answers 25 views
25 views
24 answers 40 views
40 views
1 answer 168 views
168 views
0 answers 218 views
218 views
0 answers 42 views
42 views
54 answers 39 views
39 views
15 answers 62 views
62 views
2 answers 25 views
25 views
0 answers 30 views
30 views
0 answers 276 views
276 views
1 answer 18 views
18 views
1 answer 59 views
59 views