Решение
Найдём производную
1) f(x)’ = (x-2)’ + (3/2 * x-2/3)’ - (4*x-1/2
)’ + (3x)’ – (2*x5/2)’ =-2*x-3 +
3/2*x-5/3 – 4*x/3/2 + 3 – 2*x3/2 ;f’ (1) = 2
– 3/2+ 4 + 3 + 2 =10 ½
2) f’(u) = (u2 +
3)’ * (u2 -1)1/2 + (u2 + 3) *( (u2
-1)1/2)’= 2u*(u2 -1) + ½((u2 -1)-1/2
* (u2 + 3) ;f(2) = 4*(3)1/2 + ½* (3)-1/2 *7 = 31/2√3
3) f’(x) =(x’ *(1
- √x2 +1) – x* (1 - √x2 +1)’ ) /
(1 - √x2 +1)2 = 1 - √x2 +1 – x*(1/2(x2 +1)-1/2 / (1 - √x2 +1)2 f’(√3) = (1 –
2 - √3*(1/2*1/2)/(1 – 2)2 = -(1 + √3/4)4) f’ (x) = (√ex )’ * lnx2 + √ex * (lnx2 )’ = ½*ex * nx2 + 2 √ex ;f’ (1) = 0+2 = 25)
Ускорение равно второй производной от S
S’ = 6t2 – 6t
S’’ = 12t – 6
Ускорение а = 12*3 – 6 = 30м/с