Question

Найти производную функции:
1) f(x) = x^10
2) f(x) = -6x^2
3) f(x) = -6x^5 - 4x^4 - 3x + 27
4) f(x) = (x^4 - 3)(x^3+4)
5) f(x) = (3 - 2x)^7
6) f(x) = sin 7x
7) f(x) = cos^2x
8) f(x) = cosx + sinx

Answer 1

1) f'(x}=10x^9

2)f'(x}=-12x

3)f'(x}=-30x^4-16x^3-3

4)f'(x}=(x^4-3)'(x^3+4)+(x^4-3)(x^3+4)'=4x^3(x^3+4)+(x^4-3)3x^2=7x^6+16x^3-9x^2

5)f'(x}=7(3-2x)^6(3-2x)'=-14(3-2x)^6

6)f'(x}=7cos7x

7)f'(x}=1/2+1/2(cos2x)'=-sin2x

8)f'(x}=-sinx+cosx

Answer 2

1)10х^9

2) -12х

3)-30х^4- 16х^3-3

4)3х^2(х^4-3)+4х^3(х^3+4)= 3х^6-9х^2+4х^6+16х^3= 7х^6-9х^2+16х^3

5)7(3-2х)^6*2= 14(3-2х)

6)соs7x

7)-sin^2x

8)cosx-sinx