Differentiate cos(2x^3)/3x
Using quotient rule y = u/v - dy/dx = (v.du/dx - u.dv/dx)/v2.u = cos(2x3) , a = 2x3. du/da = -sin(a), da/dx = 6x2. From chain rule, we know that du/dx = du/da . da/dx, so du/dx = -6x2sin(2x3). We know that dv/dx = 3. We now have all the necessary terms to configure dy/dx: dy/dx =( 3x . -6x2sin(2x3)-3cos(2x3))/9x2 = (-18x3sin(2x3) - 3cos(2x3))/9x2
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