JEOPARDY

Regla de cadena

10

y = (5x⁵+2)⁴

y¹ = 100x⁴ (5x⁵ + 2)³

20

y = (-5x - 3)^-2

y¹ = 10 (-5x - 3)^-3

30

(8x⁴ + 7x²)^3/2

y¹ = 48x³ + 21x (8x⁴ + 7x²)^1/2

40

y = (5/3x⁴ + 4√x)³

y¹ = 20x³ + 6x^-1/2 (5/3x⁴ + 4√x)²

50

(3/2x⁵ + 6 ⁴√x) ^-3/4

y¹ = -45/8x⁴ - 9/8x^-3/4 (3/2x⁵ + 6 ⁴√x)^-7/4

Regla del producto

10

f (x) = (2x + 3) (4x − 1)

f¹ (x) = 16x + 10

20

g (x) = (x² + 2x) (3x − 5)

g¹(x) = 9x² + 12x − 10

30

h (x) = (x³ + 2) (5x² −4x + 1)

h¹ (x) = 15x⁴ − 12x³ + 13x² − 8x + 2

40

y = (x^4/5 + 2x) (x³)

y¹ = 5/4x^14/5 + 2x³+ 3x^9/5 + 6x³

50

y = (√23x³ - 13x⁴) (4x⁵)

y¹ = 32√23 x⁷ − 468x⁸

Regla del cociente

10

f (x) = (2x +3) / (4x - 1)

f¹ (x) = -14 / (4x − 1)²

20

g(x) = (x²+2x) / (3x−5)

g¹(x) = 3x² − 16x + 6 / (3x − 5)²

30

h(x) = (x³ + 2) / (5x² − 4x + 1)

h¹(x) = 15x⁴ − 22x³ + 3x² + 4x + 2 / (5x² − 4x + 1)²

40

y = (x^4/5 + 2x) / (x³)

y¹ = 4x^14/5 + 10x³ − 15x^9/5 − 30x³ / 5x⁶

50

y = (√23x³ - 13x⁴) / (4x⁵)

y¹ = −14√23 x⁷ − 156x⁸ / 8x¹⁰

Regla de la potencia

10

y = x⁴

y¹ = 4x³

20

y = 8x^-3

y¹ = -24x^-4

30

y = 4x⁵ +x

y¹ = 20x⁴ +1

40

f (x) = 4x⁴ − 5x − 3

f¹ (x) = 16x³ − 5

50

y = 5/4x^2/3

y¹ = 5/6x^1/3

Trigonométricas

10

y = tan x⁴

y¹ = 4x³ sec² 2x⁴

20

f(x) = sen x^1/2

f(x) = 1/2x^-1/2 cos x^1/2

30

y = cos 6/7x^-8

y¹ = -48/7x^-9 sin x^-8

40

f (x) = tan 9x^5/3 

f (x) = 15x^2/3 sec² 9x^5/3

50

f (x) = cos 27/8x^8/6

f (x) = -9/2x^1/3 sin 27/8x^8/6