Mate

Ejercicios.

1. g(t) = 1

t³

g(t) = tˉ³ g(t)= -3tᶺˉ4

g(t) = - 3

tᶺ4

2. H(x)= е× - xᶺ4 + ℓn×

H¹(x)= е× - 4x³ + 1/x

3. F(x)= √x . ℓn×

f(x) = √x =x½ˉ¹ g(x)= ℓn×

f¹(x)= 1/2x ˉ½ g¹(x) = 1

f¹(x)= 1 xˉ½ x

2

f¹(x)= 1

2x½

y¹=f(x) g¹(x) + g(x) f¹(x)

y¹= x½ . 1 + ℓn× . 1

1 x 1 2x½

1 + ℓn×

y¹= x½ = 1 x½ 2x½

xᶺ2/2 x½

1 1 + ℓn×

X½ 2

Deriva las siguientes funciones básicas

1.f(x)=5 f¹(x)=0

2.f(x)=2x f¹(x)= -2

3.f(x)= -2x+2 f¹(x)= -2

4.f(x)= -7x - 3 f¹(x)= - 7

2

5. f(x) = -2x – 5 f¹(x)= - 4x

6. f(x)= 2xᶺ4 + xᶺ3 - xᶺ2 + 4= 8xᶺ3 + 3xᶺ2 – 2x

7. f(x) = xᶺ3 + 2

3

(xᶺ3 + 2)(0) – 3 (3xᶺ2) = -9xᶺ2 = -xᶺ2

9 9

8. f(x) = 1

3xᶺ2

1xᶺ-2 = -2xᶺ-3 = -2

3 3 3xᶺ3

9. f(x) = x+1 = (x+1) (1) + (x+1) (1) = 2

x-1 (x-1) ᶺ (x-1) ᶺ2

10. f(x) = (5xᶺ2 – 3) (xᶺ2 + x + 4) = (5xᶺ2-3)(2x+1) + (xᶺ2+x+4)(10x)

11- f(x) = (xᶺ2-1)(xᶺ3 + 3x)

= (xᶺ2-1)(3x+3) + xᶺ3 + 3x(2)

= 5xᶺ4 + 6xᶺ2 – 3

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