Given y=(1+x^3)^0.5, find dy/dx.

In order to solve this question, we need to use the chain rule when differentiating. The chain rule formula is dy/dx= (dy/du)(du/dx). Let u=1+x³Differentiating with respect to x gives du/dx=3x²We now have y=u^0.5Differentiating with respect to u gives dy/du=0.5u^-0.5=0.5(1+x³)^-0.5Therefore dy/dx= (dy/du)(du/dx)= 0.5(1+x³)^-0.5*(3x²)= 1.5x²*(1+x³)^-0.5