Question

(40 ) решить ! нужно решить производную а) f(x)=(2x+3) b) f(x)= c)f(x)= d) y=-3log₄x

Answer 1

А) f(x)=(2x+3) ·√(x + 4)     f'(x)= 2·√(x + 4) + (2x + 3)/(2√(x + 4)) =
= (6x + 19)/(2√(x + 4))

b) f(x)= 1/x² + 1                 f'(x) = -2/x³

c) f(x)= (2x + 3)/(6x - 8)      f'(x) = (2(6x - 8) - 6(2x + 3))/(4(3x - 4)²) =
= -17/(2(3x - 4)²)

d) y = - 3log₄x   y =  log₄ (1/x³)               y' = -3/(x ln4)  

Answer 2

1.  f'=(uv)'=u'v+v'u   u=2x+3  u'=2      v=√(x+4)   v'=1/2√(x+4)
f'=2*√(x+4)+(2x+3)/2√(x+4)
2. f'=x^(-2)+1   f'=-2x^(-3)
3. f'=(u/v)'=1/v²[u'v-v'u]   u=2x+3  u'=2     v=6x-8  v'=6
    f'=1/(6x-8)²[2(6x-8)-6(2x+3)]
4. y'=-3/(xln4)