actividades

Transcribir ejemplos de derivadas básicas, ejemplos derivadas compuestas y lo visto en clase.
- Deriva las Siguientes Funciones básicas.

1. F(x)= 5 F’(x)= 0
2. F(x)= -2x F’(x)= -2
3.F(x)= -2x+2 F’(x)= -2
4. F(x)= -7/2x-3 F’(x)= -7/2
5. F(x)= -2x²-5 F’(x)= -4x
6. F(x)= 2x4+x3-x2+4 F’(x)= 8x3+3x²-2x
7. F(x)= (x3+2)/3 F’(x)= ( (f)g’-g(f’) ) / g²= ( (x3+2)(0) – 3 (3x²) ) / 3²
= -9x² / 9 = -x²
8. F(x)= 1 / 3x² F’(x)= 1 / 3x² = 1x-2 / 3 = -2X-3 / 3
= -2 / 3x39. F(x)= x+1 / x-1 F’(x)= 2 / (x-1)2

10. F(x)= (5x²-3) (x²+x+4) F’(x)= ( f(x) * g’(x) ) + ( g(x) * F’(x) )
= (5x²-3) ( 2x+1) + (x²+x+4) (10x)

11.F(x)= (x²-1) (x3+3x) F’(x)= (x²-1) ( 3x²+3) + (x3+3x) (2x)
= (3x4+3x²-3x²+2) + (2x4+6x²)
= 5x4+6x²+2

EJEMPLOS

1.F(X)= (3x²+2)3 y’= h*f((x))n-1 * f’(x)
1. = 3*(3x²+)² *6x
2. = 18x(3x²+2) ²
2. F(x)= (5x+4x²)3 y’= 3*(5x+4x²)² * (5x+8x)
a. = 15+24x (5x+4x²)²
3. F(x)= (x3+4x²) ( 5x+4x²)33(5x+4x²)*5+8x
a. Y’= (x3+4x²) ( (24x+15)(5x+4x) ² ) + ( (5x+4x²) )3 (x3+4x²) ( 3x²+8x) )
4. Y= ln (ex+x-3) y’= 1 / (ex+x-3) * (ex+1)
a. = (ex+1) / (ex+x-3)
5. Y= 6 x/lnx x / lnx = (lnx)-1/ (lnx) ²
1. Y’= 6 1/lnx * ln6 * ( lnx-1 / (lnx) ² )
6. F(x)= ( (x²-1) / (x²-1)3 f’(x) = 3(x²-1 / x²+1 ) ² =0
7. F(x)= cos(3x) F’(x)= - sen3x*3 = -3sen3x





DERIVACIONESIMPLICITAS
Encontrar dy/dx
1. x²+y² =9 2x+2yy’=0 y’= +2x / 2y y’= -x/y
2. 5xy-y²+9x=7y3+5 5xy’+5y-2yy’+9=21y²y’ = 5xy’-2yy’-21y²y’=-9-5y
= y’ (5x-2y-21y²) =-5y-9 y’= +5y-9 / (5x-2y-21y²)
= y’= 5y+9 / -5x+2y+21y²
3. 9x²=y3+3x 18x=3yy’+3 = -3yy’=-18x+3 y’=18x+3 / 3y
4. Se tiene una alberca con las siguientes...