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+x3

Differentiating with respect to x gives du/dx=3x2

We now have y=u0.5

Differentiating with respect to u gives dy/du=0.5u-0.5=0.5*(1+x3)-0.5

Therefore dy/dx= (dy/du)*(du/dx)= 0.5*(1+x3)-0.5*(3x2)= 1.5x2*(1+x3)-0.5

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