Derivadas ð
1. y= ðð = dy=
â(ð¥ 3 )(0)â(3ð¥ 2 )(5) (ð¥ 3 )2
=
15ð¥ 2 ð¥6
=
15 ð¥4
2. y=(ðð â ððð )(ðð + ð)ð yÂŽ= (5ð¥ â 3ð¥ 2 )(5)(4ð¥ + 7)4 (4) + (4ð¥ + 7)5 (5 â 6ð¥) yÂŽ= (4ð¥ + 7)4 [20(5ð¥ â 3ð¥ 2 ) + (4ð¥ + 7)(5 â 6ð¥) ] yÂŽ= (4ð¥ + 7)4 [ 100ð¥ 2 â 60ð¥ 2 + 20ð¥ â 24ð¥ 2 + 35 â 42ð¥] yÂŽ=(4ð¥ + 7)4 [ 84ð¥ 2 + 78ð¥ + 35] 3. y= (ð â ð)(ðð â ð) yÂŽ=(ð¥ â 2)(2) + (2ð¥ â 3)(1) yÂŽ=2ð¥ â 4 + 2ð¥ â 3 yÂŽ= 4x -7
4. y= 29x5 yÂŽ= 145x4
5.
(ðð +ð)ð
(8âð¥ 2 )4(ð¥ 3 +5)3 (3ð¥ 2 )â(ð¥ 3 +5)4 (â2ð¥)
=
ðâðð (8âð¥ 2 )2 2x(ð¥ 5 +5)3 [6ð¥(8âð¥ 2 )+(ð¥ 3 +5)]
yÂŽ=
(8âð¥ 2 )2
2ð¥(ð¥ 3 +5)3 (48ð¥â6ð¥ 3 +ð¥ 3 +5)
yÂŽ=
(8âð¥ 2 )2
2ð¥(ð¥ 3 +5)3 (â7ð¥ 3 +48ð¥+5)
yÂŽ=
(8âð¥ 2 )2
ðð +ðð+ð
6. h(x)=
âð 3
3
1
â1
= ð¥ 2 + 4ð¥ 2 + 3ð¥ 2
3
1
1 2
1
1 2
hÂŽ(x)= ( ) ð¥ 2 + ( )(4)ð¥ 2â2 (â )(3)ð¥ â2â2 2 2 2