How to differentiate y=2x(x-2)^5 to find dy/dx?

Firstly, you should formulate the problem by using the product rule, which is: dy/dx = u'v + v'uBy assigning u=2x and v=(x-2)⁵ , the terms u' and v' can be obtained knowing that u' simply means differentiation of u with respect to x and v' is the differential of v with respect to x.u' = 2;v' = 51(x-2)^4Combining the terms, dy/dx = 2(x-2)⁵ + 10x(x-2)⁴ which is in its simplest form and provides the answer for subsequent question parts.