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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