taller full calculo diferencial
TRANSCRIPT
Cálculo Diferencial Taller de Derivadas
A-Mediante la definición, halle la derivada de:
1. f ( x )=√5 x−7
2. f ( x )=7 x−2
3. f ( x )=4 x3−7 x2+9
4. f ( x )=7 x−2−2 x4+3 x3
3 x−1
5. y=sen (3 x )
6. y=sec(8 x )
7. y= tan(2 x )
8. f ( x )=5 x4
9. f ( x )= 5
(3 x+4 )2
10. y= ln(5−3 x )
B-Mediante reglas de cálculo, halle la derivada de:
1. y=arcsen (x )2
2. y=4√sen3 (eln ( 3 x ) )
3. y=4 x−x2−3 x3+ x
ex
4. y=ex ln x
5. y=tan (ex )−3 ln (e2 x )
6. y= (2x−3 ) (3 x−2 )+4x
7. y=4 ln2 (sec (2 x+1 ) )
8. y=sen [ cos (e tan (2 x ) ) ]
9. y= xx3−4+e3 x
10. y=esen ( 5 x )+8cos ( 4 x )
11. y=11−3−5√ x3+cos (2 x )
12. y=3√ ln (cos (8 x2))
13. y=csc2 (5 x )⋅cot3 (5x )
C- Derive implícitamente:
14. 2 y=x7e x cos3 y
15.
xy+ yx=6 xy
16. y2+x3=xe y−sec (πy )
17. y= (3 y )x
18. x2+ y2=5
19. 2 x2 y−5 x+ y2=2−x3
20. 3− y2− y=x3−x2−sen3 x+4 ln y
D-Halle la ecuación recta tangente y normal
21. y=3 x−5
x2+7 p(0 , -5)
22⋅y=√3 x−7
23⋅y=(2x+5 )3
24⋅y3−xy2+cos ( xy )=2
25⋅y=ln [sen (3x ) ]
p (11/3 ,−2 )
p (−1,3 )
p (0,1 )
p (π /6,0 )
A2
Puto A3
Punto A4