Question

DIFFERENTIATE 2X^6 (1-2X)^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To differentiate the expression 2x^6(1-2x)^2, we will need to use the product rule and chain rule of differentiation.

Let's start by expanding the expression (1-2x)^2:
(1-2x)^2 = (1-2x)(1-2x)
= 1 - 2x - 2x + 4x^2
= 1 - 4x + 4x^2

Now, we can rewrite the original expression as:
2x^6(1-2x)^2 = 2x^6(1 - 4x + 4x^2)

Now, let's differentiate the expression using the product rule:
d/dx [2x^6(1 - 4x + 4x^2)] = 2x^6 d/dx(1 - 4x + 4x^2) + (1 - 4x + 4x^2) d/dx(2x^6)
= 2x^6(-4 + 8x) + (1 - 4x + 4x^2)(12x^5)
= -8x^6 + 16x^7 + 12x^5 - 48x^6 + 48x^7 + 48x^6
= 16x^7 - 40x^6 + 12x^5

So, the derivative of 2x^6(1-2x)^2 is 16x^7 - 40x^6 + 12x^5.