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=u0.5Differentiating 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
