JEOPARDY

Regla de la potencia

100

Y= 5x⁴ 

20x³

200

Y= 8x² — 6x + 1

16x — 6

300

Y= -6x⁵

-30x⁴

400

y= x¹⁸

18x¹⁷

500

12x^-3 + 8x⁴

-36x^-4 + 32x³

Regla de la cadena

100

Y=(4x³ + 1)⁴

4(4x³ + 1)³ (12x² ) 

200

Y=(5x⁵ + 1)²

2(5x² + 1)(25x⁴)

300

Y= (3x³  - 9)(x² + 3)

(3x³ - 9)(2x)+(x² + 3)(9x²)

400

Y=(x⁵ + 3)⁴

4(x⁵ + 3)³ (5x⁴ )

500

Y=(5x² + 1) x⁴ 

(5x² + 1) (4x³ ) + (x⁴)(10x)

Regla del producto

100

Y=(-4x²)(x²+1)

(-4x²)(2x)+(x³+1)(-8x)

200

Y=(5x⁴)(x² - 3x + 1)

(5x⁴)(2x-3x)+(x²-3x+1)(20x³)

300

Y=(x+x)(x-1)⁴ 

(x+x)(4(x-1)³) + (x-1)⁴ (1+1)

400

Y=(5x-4)⁹(3x-2)⁶

(5x-4)⁹(6(3x-2)⁵(3))+(3x-2)⁶(9(5x-4)⁸(5))

500

Y=x²(2x+1)³

(x²)(3(2x+1)²(2))+((2x+1)³)(2x)

Regla del cociente

100

Y=2X³ -1/X

(2x³-1)(1)-(x)(6x²)/x²

200

y=x^1/2/x²+1

(x^1/2)(2x)-(x²+1)(x^1/2)/(x²+1)²

300

y=(x²/x+1)²

(x+1)²(2x)-x²(2(x+1))/((x+1)²)²

400

y=(2x-1)³/x²+1

(x²+1)(6(2x-1)²)-(2x-1)²(2x)/(x²+1)²

500

y=(2-2x²/x^1/2)4

(x^1/2)(-16x(-2x²+2)³)-(-2x²+2)⁴(112/x^1/2)/x

Derivadas y logarítmicas y Exponenciales

100

Y=e^x7

e^x7 (7x⁶)

200

Y= e^8x2

e^8x2(16x)

300

Y=e^3x3+2x

e^3x2+2x(9x² + 2)

400

Y=2^2x2

2^2x2(4x)log4

500

Y=4^x8-7x

4^x8-7x (8x⁷-7) log 4