Differentiate the function y=(6x-1)^7

Problems of this style are solved using the chain rule.

To begin, define the quantity inside the brackets as u

u = 6x-1 such that y = u^7

It is now useful to write the chain rule. We can see

dy/dx = du/dx x dy/du

as the du 'cancel'. Now, all we need to do is differentiate two simple expressions:

du/dx = 6 and dy/du = 7u^6

Substituting these expressions back into the chain rule:

dy/dx = 42u^6

Finally, substitute u into this expression to give the final answer, 

dy/dx = 42(6x-1)^6