Differentiate y=(4x^2-1)^3
When differentiating a composite function y = (4x2-1)3 , the chain rule needs to be used.
The chain rule is dy/dx= dy/du x du/dx
In this instance we need to assign u and y in order to differentiate and get the expression for dy/dx.
We can assign u to what is in the bracket. u = 4x2 -1 . Therefore y = u3So du/dx= 8x and dy/du = 3u2 When we substitute this back into the original chain rule, we get dy/dx = 3u2 x 8xWe already have the u, which is =4x2 -1
Therefore, putting this together gets dy/dx= 3(4x2 -1)2 x 8x = 24x(4x2-1)2.
