Найти f '(1)
2) f(x)=(x+1)³ (x+2)3)f(x)=2x-1/2x+1
4)f(x)=2x²/1-7x5)f(x)=2x-3/5-4x

Предыдущий
вопрос Следующий
вопрос

1) f'(x) = 3(x+1)² 1 (x+2)³ + (x+1)³ 3 (x+2)²
= 3(x+1)²(x+2)³ + 3(x+1)³(x+2)²

Substitute x = 1 into the derivative to find f'(1):
f'(1) = 3(1+1)²(1+2)³ + 3(1+1)³(1+2)²
= 3(2)²(3)³ + 3(2)³(3)²
= 3(4)(27) + 3(8)(9)
= 3(108) + 3(72)
= 324 + 216
= 540

Therefore, f'(1) = 540.

2) f'(x) = [(2x - 1)(2) - (2x)(-2)] / (2x + 1)²
= (4x - 2 + 4x) / (2x + 1)²
= (8x - 2) / (2x + 1)²

Substitute x = 1 into the derivative to find f'(1):
f'(1) = (8(1) - 2) / (2(1) + 1)²
= (8 - 2) / (2 + 1)²
= 6 / 3²
= 6 / 9
= 2/3

Therefore, f'(1) = 2/3.

3) f'(x) = [(2x²)'(1-7x) - (2x²)(1-7x)'] / (1-7x)²
= [4x(1-7x) - 2x²(-7)] / (1-7x)²
= (4x - 28x² + 14x²) / (1-7x)²
= (-24x² + 4x) / (1-7x)²

Substitute x = 1 into the derivative to find f'(1):
f'(1) = (-24(1)² + 4(1)) / (1-7(1))²
= (-24 + 4) / (1-7)²
= -20 / (-6)²
= -20 / 36
= -5/9

Therefore, f'(1) = -5/9.

4) f'(x) = [(2x-3)(-4) - (2)(5-4x)] / (5-4x)²
= (-8x + 12 + 10 - 8x) / (5-4x)²
= (-16x + 22) / (5-4x)²

Substitute x = 1 into the derivative to find f'(1):
f'(1) = (-16(1) + 22) / (5-4(1))²
= (-16 + 22) / (5-4)²
= 6 / 1
= 6

Therefore, f'(1) = 6.