Derivadas

Page 1

Derivadas 𝟓

1. y= 𝒙𝟑 = dy=

−(𝑥 3 )(0)−(3𝑥 2 )(5) (𝑥 3 )2

=

15𝑥 2 𝑥6

=

15 𝑥4

2. y=(𝟓𝒙 − 𝟑𝒙𝟐 )(𝟒𝒙 + 𝟕)𝟓 yÂŽ= (5𝑥 − 3𝑥 2 )(5)(4𝑥 + 7)4 (4) + (4𝑥 + 7)5 (5 − 6𝑥) yÂŽ= (4𝑥 + 7)4 [20(5𝑥 − 3𝑥 2 ) + (4𝑥 + 7)(5 − 6𝑥) ] yÂŽ= (4𝑥 + 7)4 [ 100𝑥 2 − 60𝑥 2 + 20𝑥 − 24𝑥 2 + 35 − 42𝑥] yÂŽ=(4𝑥 + 7)4 [ 84𝑥 2 + 78𝑥 + 35] 3. y= (𝒙 − 𝟐)(𝟐𝒙 − 𝟑) yÂŽ=(𝑥 − 2)(2) + (2𝑥 − 3)(1) yÂŽ=2𝑥 − 4 + 2𝑥 − 3 yÂŽ= 4x -7

4. y= 29x5 yÂŽ= 145x4

5.

(𝒙𝟑 +𝟓)𝟒

(8−𝑥 2 )4(𝑥 3 +5)3 (3𝑥 2 )−(𝑥 3 +5)4 (−2𝑥)

=

𝟖−𝒙𝟐 (8−𝑥 2 )2 2x(𝑥 5 +5)3 [6𝑥(8−𝑥 2 )+(𝑥 3 +5)]

yÂŽ=

(8−𝑥 2 )2

2𝑥(𝑥 3 +5)3 (48𝑥−6𝑥 3 +𝑥 3 +5)

yÂŽ=

(8−𝑥 2 )2

2𝑥(𝑥 3 +5)3 (−7𝑥 3 +48𝑥+5)

yÂŽ=

(8−𝑥 2 )2

𝒙𝟐 +𝟒𝒙+𝟑

6. h(x)=

√𝒙 3

3

1

−1

= 𝑥 2 + 4𝑥 2 + 3𝑥 2

3

1

1 2

1

1 2

hÂŽ(x)= ( ) 𝑥 2 + ( )(4)𝑥 2−2 (− )(3)𝑥 −2−2 2 2 2


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