Sec 3 maths(I start to learn this topic yesterday only=I do)

Rules:

Product Rule:
d f(x)g(x) / dx = [d f(x) / dx] * g(x) + f(x) * [d g(x) / dx]

Power Rule:
d x^n / dx = n * x^(n-1)

Chain Rule:
d f[g(x)] / dx = [d f(u) / du] * [d g(x) / dx] ----- let u = g(x)

Answer:
c)

d [(1-2x)(3x+2)^4] / dx
= [d (1-2x) / dx] * (3x+2)^4 + (1-2x) * [d (3x+2)^4 / dx] ----- product rule
= (-2) * (3x+2)^4 + (1-2x) * [4(3x+2)^3](3) ----- power rule and chain rule
= [(3x+2)^3] * [(-2)(3x+2) + (1-2x)(4)(3)] ----- factor (3x+2)^3 out
= [(3x+2)^3] * (-6x-4+12-24x)
= [(3x+2)^3] * (-30x+8)
= [(3x+2)^3] * [2 (-15x+4)]
= 2 * (3x+2)^3 * (4-15x)


k)

d [(x^2-3x+4)(1-x/2)^2] / dx
= [d (x^2-3x+4) / dx] * (1-x/2)^2 + (x^2-3x+4) * [d (1-x/2)^2 / dx] ----- product rule
= (2x-3) * (1-x/2)^2 + (x^2-3x+4) * [2(1-x/2)](-1/2) ----- power rule and chain rule
= (1-x/2) * [(2x-3)(1-x/2) + (x^2-3x+4)(2)(-1/2)] ----- factor (1-x/2) out
= (1-x/2) * (2x-x^2-3+3x/2 - x^2+3x-4)
= (1-x/2) * (-2x^2+13x/2-7)


f)

d [(4x-1)(3x^2+1)^(1/2)] / dx
= [d (4x-1) / dx] * (3x^2+1)^(1/2) + (4x-1) * [d (3x^2+1)^(1/2) / dx] ----- product rule
= (4) * (3x^2+1)^(1/2) + (4x-1) * [(1/2)(3x^2+1)^(-1/2)](6x) ----- power rule and chain rule
= (3x^2+1)^(-1/2) * [(4)(3x^2+1) + (4x-1)(1/2)(6x)] ----- factor (3x^2+1)^(-1/2) out
= (3x^2+1)^(-1/2) * (12x^2+4 + 12x^2-3x)
= (3x^2+1)^(-1/2) * (24x^2-3x+4)
= (24x^2-3x+4) / [(3x^2+1)^(1/2)]