Differentiate y= (6x^2 - 5)^(3/2) with respect to x
Simplify the equation to y=u3/2 where u = 6x2 -5Use the chain ruledy/dx = dy/du x du/dxdy/du = (3/2)u1/2du/dx = 12x - 0Therefore dy/dx = (3/2)u1/2 x 12xBut u = 6x2-5 so substitute that into the derivative.dy/dx = 3/2(6x2-5)1/2 x 12xSimplify to dy/dx= 18x(6x2-5)1/2
