Question

Найдите производные функции:
f(x)=10(4-5x)^10-(5-4x)^30

Answer 1

1) f(x)=(4√x +3)(4√x -3)+2x² = 16x - 9 + 2x² 

f'(x)=(16x - 9 + 2x²)' = 16 + 4x = 4(4 + x) 

 

2) f(x)=(x^2+5)(x^2-4)+2√x = x⁴ - 4x² + 5x² - 20 + 2√x = x⁴ + x² + 2√x - 20 

f'(x)= ( x⁴ + x² + 2√x - 20 )' = 3x³ + 2x + 1/√x

 

3) f(x)=√2x^2-(3x-2)5x+1)-√x = √2 x² - 15x² +10x + 1 -√x 

f'(x)= (√2 x² - 15x² +10x + 1 -√x )' = 2√2x - 30x + 10 - 1/2√x = x(2√2 - 30) +10 - 1/2√x