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INSTITUTO TECNOLÓGICO DE AGUASCALIENTESEJERCICIOS DE DERIVADAS.

Materia: Cálculo diferencial.

Ingeniería industrial.

Grupo #1

Aguascalientes, Ags. a 4 de diciembre de 2013.

1

1.-f ( x )=13√x5

f ( x )= x-53

f ´ ( x )= -53

(x)- 83

f ´ ( x )=- 5

33√x8

2.- f ( x )= x

4 x2−3

f ´ ( x )= 4 x2−3 (1 )−( x )8 x2

( 4 x2−3 )2

f ´ ( x )= 4 x2−3−8 x2

(4 x2−3)2

f ´ ( x )= −4 x2−3(4 x2−3)2

f ´ ( x )= −1

(4 x2−3)

3.- f (x )=( x+5x−2 )

2

f ´ ( x )=2( x+5x−2 )[ x−2 (1 )−(x+5)(1)

(x−2)2 ]f ´ ( x )=2( x+5

x−2 )[ x−2−x−5

(x−2)2 ]f ´ ( x )=2( x+5

x−2 )[ −7

(x−2)2 ]f ´ ( x )=2

−7(x+5)(x−2)3

f ´ ( x )=2−7 x−35

(x−2 )3

f´(x)=−14 x−70

( x−2)3

4.- f ( x ) = x−5

x3+x

f ´ ( x )=(x3+x ) (1 )−(x−5)(3 x2+1)

( x3+x )2

f ´ ( x )=( x3+x )−3x3−x+15 x2+5¿ ¿( x3+x )2

f ´ ( x )=−2x3+15 x2+5¿ ¿(x3+x)2

5.- f ( x )=√x2−25

f ( x )=¿

f ´ ( x )=12¿

f ´ ( x )= 2 x

2√x2−25

f ´ ( x )= x

√ x2−25

6.- f ( x )=x √2x+1

f ( x )=x ¿

f ´ ( x )=x ¿ (1)

f ´ ( x )= 2 x

2√2x+1+√2 x+1

f ´ ( x )= x+2x+1

√2x+1

2