Jawaban:

a. y = 2x³ - 4x² + 7x^5

dy/dx = 2.3x² - 4.2x + 7.5 x^4

dy/dx = 6x² -8x + 35 x^4

b. y = 9-3x + 6x²

dy/dx = -3 + 6.2 x

dy/dx = -3 + 12x

c. y = (3x-2)³

dy/dx = 3.(3x-2)².3

dy/dx = 9(3x-2)²

d. y = 3(2x + 4)^5

dy/dx = 3.5 (2x + 4)^4. 2

dy/dx = 30 (2x + 4)^4

e. y = 8 (x² + x) ^1/2

dy/dx = 8.1/2 (x² + x) ^(-1/2) (2x + 1)

dy/dx = 4(2x+1)/√(x² + x)

dy/dx = (8x + 4)/√(x² + x)

f. y = 1/(3x² -4)

dy/dx = ln (3x² -4)

g. y= (4x -1)^7

dy/dx = 7(4x-1)^6. 4

dy/dx = 28 (4x-1)^6

h. y = (4x³ -x²)³

dy/dx = 3(4x³-x²)².(12x²-2x)

dy/dx = 3(12x²-2x)(4x³-x²)²

dy/dx = (36x²-6x)(4x³-x²)²

i. y = 2e^(x²)

dy/dx = 2.2x e^(x²)

dy/dx = 4x e^(x²)

j. xy-x² + y² = 0

x dy/dx + y -2x + 2y dy/dx = 0

(x + 2y) dy/dx = 2x -y

dy/dx = (2x - y) / (x + 2y)