A) y=7x⁶ - 2x+10
y' = 42x⁵ -2
б) f(x)=x² sinx
f(x)' = (x²)' sinx + x² (sinx)' = 2x sinx + x² cosx
в) f(x)=3x-5
1+4x
f(x)' = (3x-5)' (1+4x) - (3x-5) (1+4x)' = 3(1+4x) - 4(3x-5) =
(1+4x)² (1+4x)²
= 3+12x-12x+20 = 23
(1+4x)² (1+4x)²
г) f(x)=6/x - 6√x +4x¹⁷
f(x)' = -6 - 6 + 68x¹⁶
x² 2√x
д) f(x)=(1+x³)*2√x
f(x)' = (1+x³)' *2√x + (1+x³) *(2√x)' = 6x²√x + 1+x³ =
√x
=6x²√x √x +1+x³ = 6x³+1+x³ = 7x³+1
√x √x √x