Penjelasan dengan langkah-langkah:

a) f(x) = (x²-x)(x³+2)

=> dy/dx

= [d(x²-x)] × (x³+2) + (x²-x) × [d(x³+2)]

=> (2x)(x³+2) + (x²-x)(3x²)

=> 2(x^4) + 4x + 3(x^4) - 3x³

<=> 5(x^4) - 3x³ + 4x

b) f(x) = (x³-1)(x^4 + x²)(3x²-5x)

=> (x³-1)(x²)(x²+1)(x)(3x-5)

=> (x³)(x³-1)(3x-5)

=> (x^6 - x³)(3x-5)

dy/dx => [d(x^6 - x³)](3x-5) + (x^6 - x³)[d(3x-5)]

<=> [6(x^5) - 3x²](3x-5) + 3[x^6 - x³]

=> ( 18(x^6) - 30(x^5) - 9x³ + 15x² ) + (3(x^6) - 3x³)

=> 21(x^6) - 30(x^5) - 12x³ + 15x²

c) f(x) = (3x-5)(x³+4x²-3)

dy/dx = [d(3x-5)](x³+4x²-3) + (3x-5)[d(x³+4x²-3)]

=> 3(x³+4x²-3) + (3x-5)(3x²+8x)

=> (3x³+12x²-9) + (9x³+9x²-40x)

=> 12x³+21x²-40x-9

d) f(x) = (x-2) / (x²+2)

<=> dy/dx => [d(x-2) × (x²+2) - (x-2) × d(x²+2)] / (x²+2)²

=> [(x²+2) - (2x)(x-2)] / (x²+2)²

=> (-x²+4x+2) / (x²+2)²

e) f(x) = (x²+4)(2x-1)

dy/dx

=> [d(x²+4) (2x-1) - (x²+4) d(2x-1) ] / (2x-1)²

=> [(2x)(2x-1) - (x²+4)(2)] / (4x²-4x+1)

=> [(4x²-2x) - (2x²+8)] / (4x²-4x+1)

=> (2x²-2x-8) / (4x²-4x+1)

Semoga membantu yh :)