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.
