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
JL
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