Question

Помогите решить пожалуйста

Answer 1

Ответ:

1)

у=2х^7-8х+3

у'=(2х^7)'-(8х)'+(3)'=2×7х^6-8+0=14х^6-8

2)у=6х^5-3/х+2×х^1/2

у'=(6х^5)'-(3/х)'+(2х^1/2)=6×5х^4-3lgx+2×1/2x^-1/2=

=30x^4-3 lgx+x^-1/2=30x^4-3 lgx+1/на корень из х

3)у=х^2 × cosx

(u+v)' =u'v+uv'=(x^2)'×cosx + x^2×(cosx)'=2x×cosx+x^2×sinx=x(2cosx+sin^2x)

4)

f(x)=x^2+2/x-1

f'(x)=(x^2)' × x-1 - x^2 × (x-1)'/(x-1)^2

f'(x)=2x × (x-1) - x^2 × 1/(x-1)(x-1)

2x-x^2/x-1

5)

f(x)=6x^2-3x-5/x

f'(x)=(6x^2)'-(3x)'-(5/x)'=6×2x-3-5 lgx=12x-3-5 lgx

6)f(x)=4×x^1/2-x/5+2

f'(x)=(4x^1/2)'-(x/5)'+(2)'=4×1/2x^(-1/2)-1/5+0=2x^-1/2

-1/5