Объяснение:
а) f'(x)= 54x⁸+8
б) f'(x)= (x⁶-x²)'sin(x)+(x⁶-x²)*(sin(x))'= sin(x)*(6x⁵-2x)+cos(x)(x⁶-x²)= sin(x)*2x(3x⁴-1)+cos(x)*x²(x⁴-1)
в) f'(x)= (cos(x)'(9-x²)-cos(x)*(9-x²)')/(9-x²)²= (-sin(x)(9-x²)+cos(x)*2x)/(9-x²)²
г) f'(x)= 6/cos²(6x)
д) f'(x)= 1/2√8x⁵-x³ * (40x⁴-3x²)= (40x⁴-3x²)/2√8x⁵-x³
е) f'(x)= 8(5x-6)⁷*5= 40(5x-6)⁷
Объяснение:
а) f'(x)= 54x⁸+8
б) f'(x)= (x⁶-x²)'sin(x)+(x⁶-x²)*(sin(x))'= sin(x)*(6x⁵-2x)+cos(x)(x⁶-x²)= sin(x)*2x(3x⁴-1)+cos(x)*x²(x⁴-1)
в) f'(x)= (cos(x)'(9-x²)-cos(x)*(9-x²)')/(9-x²)²= (-sin(x)(9-x²)+cos(x)*2x)/(9-x²)²
г) f'(x)= 6/cos²(6x)
д) f'(x)= 1/2√8x⁵-x³ * (40x⁴-3x²)= (40x⁴-3x²)/2√8x⁵-x³
е) f'(x)= 8(5x-6)⁷*5= 40(5x-6)⁷