Derivadas (María José, Emilio Echauri,Dayana y America)

Potencia

100

y= -4x

y' =-4

200

y= 5x

y'= 5

300

y= 2x⁴

y'= 8x³

400

y= 5x^1/2

y'= (5/2) x^-1/2

500

y= (1/2) x^3/4

y'= (3/8) x^-1/4

Cadena

100

y= (3x²+2)³

y'= 18x (3x²+2)²

200

y= (-3x²+5)⁴

y'= -24x (-3x²+5)³

300

y= (-5x⁴+3)³

y'= -60x³ (-5x⁴+3)²

400

y= (4x⁵+5)^-4

y'= -80x⁴ (4x⁵+5)^-5

500

y=(5x+4)^1/5

y'= 1(5x+4)^-4/5

Producto

100

y=(3x³)(3x³ -2)

y'= 54x⁵ - 18x²

200

y= (x⁵+3)(x⁴)

y'=9x⁸+12x³

300

y=(-5x⁵-3)(-3x³+4)

y'=120x⁷-100x⁴+27x²

400

y=(4x⁵+2^2/3+4)(2x²+5)

y'=56x⁶+100x⁴+(32/3)x^5/3+(20/3)x^1/3+16x

500

y=(x⁴+(⁴√x)+2)(3x⁵-4)

y'=27x⁸-16x³+(63/4)x^16/4-x^-3/4+30x⁴

Cociente

100

y= (1)/(x-1)

y'=(-1)/(x-1)²

200

y= (3x⁵)/(3x³+2)

y'= (18x⁷+30x⁴ )/ (3x³+2)²

300

y=(4x⁵)/(5x⁴+5)

y'= (20x⁸+100x⁴ )/ (5x⁴+5)²

400

y= (x⁵)/(x³+4)

y'= (2x⁷+20x⁴) /(3x³+4)²

500

y=(3x⁵-4x⁴+4x³)/(5x³-2)

y'=(30x⁷-20x⁶-30x⁴+32x³-24x²)/(5x³-2)²

Trigonométrica

100

y=sin 5x³

y'=15x² cos 5x³

200

y=cos 3x⁵

y'=-15x⁴ sen 3x⁵

300

y=sin 5x⁴

y'=20x³ cos 5x⁴

400

y=tan 4x³

y'=12x² sec² 4x³

500

y=tan x⁴

y'=4x³ sec² x⁴