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