Jeopardy calculo

Regla de la potencia

100

y=x⁶

y¹=6x⁵

200

2x⁴-3

8x³

300

y=5x⁷-7x+2

y¹=35x⁶-7

400

y=3/2x³-4x³-35

y¹⁼9/2x²-12x²

500

3/x⁵+5/7x²+25x⁴

-15/x⁶+10/7x+100x³

Regla de la cadena

100

y=5/(3x²-2)⁵

y'=150x/(3x²-2)⁶

200

y=9/(x²+5)³

-54/(x²+5)³

300

y=-3/4(10x²-6)⁷

-105x(10x²-6)⁶

400

y=(3x²+4)(2x²-5)

y=(3x²+4)(8x³)+(2x⁴-5)(6x)

500

G(X)=3x-2x²

=3(3x-2x²)

Regla del producto

100

y=(x²+17)(6x³+10)⁶

(x²+17)(108x²(6x³+10)⁵+(6x⁵+10)⁶(2x)

200

y=(5x²+9)⁵(10x³+12)³

(5x²+9)⁵(90x²(10x³+12)²+(10x³+12)³(50x(5x²+9)⁴

300

y=(3x²+6)⁸(5x³+5)³

y¹=(3x²+6)⁸(45x²(5x³+5)²+(5x³+5)³(48x(3x²+6)⁷

400

d/dx [g(x)  h(x)]en x=-4

=7

500

f(x)=x⁴+1

g(x)= (x+1)^-1

dy/dx=- (x⁴+1)/((x+1)² )+(4x³)/(x+1)

Regla del cociente

100

f(x)=3x-5/6x+7

51/(6x+7)

200

f(x)=2x+3/5x+4

-7/(5x+4)

300

f(x)=3x²-2/5x⁵-1

-15x⁴+30x²-6x/(5x³-1)

400

f(x)=2x⁴+3x²/2x⁵-6x²

16x6-48x⁵+12x⁴-36x³-12x⁶+24x⁵-18x⁴+36x⁵/(2x⁵-6x²)²

500

f(x)=2x⁵-4x⁵/x⁸+7

4x⁷+74x⁴-56x/(x⁵+7)²

derivadas logarítmicas y exponenciales

100

d/dx[2(4x^2+5x-1)]

(8x+5)ln(2)^((4x^2+5x-1))

200

y=e^((3x^2-4)).

=6x e^((3x^2-4))

300

Sea h(x)=e^((x^3+5x^2 ).)

h´(x)= e^((x^3+5x^2))  (3x^2+10x)

400

d/dx [e^2x ].

〖2e〗^2x

500

d/dx  log⁡(5x-x^2 )

(5-2x)/((5x-x^2 )ln⁡(10))