Differentiate the folloing w.r.t.x e^x^3

y=e^x^3 Put x^3=t

Therefore, y=e^t and t=x^3

=>dy/dt=e^t , dt/dx=3x^2

=> dy/dx=dy/dt*dt/dx=e^t*3x^2=3x^2e^x^3 Ans.

Differentiate using chain rule.
d(e^x^3)/dx = d(e^x^3)/d(x^3) * d(x^3)/dx = e^x^3 * 3*x^2 = 3*(x^2)*(e^x^3)

3x^2 * e^x^3 (using chain rule)