| 2011 | | Cea 08 Pueblo Nuevo Oax.

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[EJERCICIOS DE CALCULO DIFERENCIAL] | Este trabajo contiene ejercicios del libro Calculo Direncial E Integral GRANVILLE, pág. 44-45 ejercicios del 9-36 resueltos paso a paso. |

Ejercicios de Calculo
Comprobar cada una de las siguientes derivadas.
1.- d/dx (3x4 – 2x2 + 8) =
= d/dx(3x4) - d/dx (2x2) + d/dx (8)
= 3d/dx (x4) – 2d/dx (x2) +d/dx (8)
= 3.4 x3 d/dx (x) – 2.2x d/dx(x)
= 12x3 – 4x

2.- d/dx (4 + 3x – 2x3)
= d/dx (4) + d/dx (3x) – d/dx(2x3)
= d/dx (4) + 3d/dx (x) – 2 d/dx(x3)
= 3 – 2.3x2 d/dx (x)
= 3 – 6x2

3.- d/dt (at5 – 5bt3) =
= d/dt (at5) – d/dt (5bt3)
= a d/dt (t5) – 5b d/dt (t3)
= a.5 t4 d/dt (t) – 5b.3 t2 d/dt (t)
= 5at4 – 15bt2

4.- d/dz (z2/2 – …ver más…

dx(x√a + bx)
= x d/dx (√a + bx) + √a + bx d/dx (x)
= x d/dx(a + bx)1/2 + √a + bx
= ½x (a + bx)1/2-1 d/dx (a + bx) + √a + bx
= ½x (a + bx)-1/2 [d/dx (a) + d/dx(bx)] + √a + bx
= ½x (a + bx)-1/2 [b d/dx (x)] + √a + bx
= bx/2 (a + bx)-1/2 + √a + bx
= bx/2√a+bx + √a + bx/1
= bx + 2(√a + bx)2 / 2√a + bx
= bx + 2a + 2bx / 2√a + bx
= 2a + 3b /2√a + bx

21.- d/dt (t √a2 + t2)
= t d/dt √a2 + t2 + √a2 + t2 d/dt (t)
= t d/dt (a + t2)1/2 + √a2 + t2
= ½t (a + t2)1/2-1 d/dt (a2 + t2) + √a2 + t2
= t/2 (a2 + t2)-1/2 [d/dt (a2) + d/dt (t2)] + √a2 + t2
= t/2√22 + t2 [2t d/dt (t)] + √a2 + t2
= 2t2/2√a2 + t2 +√a2 + t2
= t2/√a2 + t2 + √a2 + t2/1
= t2 + (√a2 + t2)2 / √a2 + t2
= t2 + a2 + t2 / √a2 + t2
= a2 + 2 + t2 / √a2 + t2

22 .- d/dx (a-x/a+x)
= (a+x) d/dx (a-x) d/dx (a+x)/ (a+x)2
= (a+x) d/dx (a-x) – (a-x) d/dx (a+x) /(a+x)2
= (a+x) (-1) – (a-x) (1) / (a+x)2
= -a –x –a + x / (a+x)2
= -2ª / (a+x)2

23.- d/dx (a2+x2/a2-x2)
= (a2-x2) d/dx (a2+x2) - (a2+x2) d/dx (a2-x2)/ (a2-x2)2
= (a2-x2) (2x) - (a2+x2) (-2x) / (a2-x2)2
= 2a2x – 2x3 + 2a2x + 2x3 / (a2-x2)2
= 4a2x/(a2-x2)2

24 .- d/dx (√a2+x2 / x)
= x d/dx √a2+x2 - √a2+x2 d/dx (x) / x2
= x d/dx (a2 + x2) ½ - √a2+x2/ x2
= x/2 (a2+x2) -½ (2x) - √a2+x2 / x2
= x/2 √a2+x2 - √a2+x2 /1 / x2
= x2 – (√a2 + x2)2/√a2+ x2 / x2
= x2 – a2 – x2/√a2 + x2 / x2
= -a2/√a2 + x2 / x2/1
= -a2/x2√a2 + x2

25.- d/dx (x/√a2 – x2)
= √a2 - x2 d/dx (x) – x d/dx √a2 - x2 / (√a2 – x2)2
= √a2 – x2 – x d/dx (a2 –