Question

Найдите производную
1) y=14x⁵
2) y = (3x-9)⁶
3) y = x²+7/3x-9
4) y = 13x⁶
5) y = (7x+5)⁸
6) y = x²-4/4x-5

Answer 1

Ответ:

Объяснение:

1) y=14x⁵

y'=14·5·x^(5-1)=70x^4

2) y = (3x-9)⁶

    y'=6·(3x-9)'·(3x-9)^5=6·3·(3x-9)^5=18·(3x-9)^5

3) y = x²+7/3x-9

  y'=((x²+7)'·(3x-9)-(x²+7)·(3x-9)')/(3x-9)²=(2x·(3x-9)-3·(x²+7))/(3x-9)²=(6x²-18x-3x²-21)/(3x-9)²=(3x²-18x-21)/9·(x-3)²=3(x²-6x-7)/9·(x-3)²=(x²-6x-7)/3·(x-3)²

4) y = 13x⁶

   y'=78x^5

5) y = (7x+5)⁸

  y'=8·(7x+5)^(8-1)·(7x+5)'=56(7x+5)^7

6) y = x²-4/4x-5

  у'=((x²-4)'·(4x-5)-(x²-4)·(4x-5)')/(4x-5)²=(2x·(4x-5)-4·(x²-4))/(4x-5)²=(8x²-10x-4x²+16)/(4x-5)²=(4x²-10x+16)/(4x-5)²