Differentiate y=e^(x^2+2x)

For this question the chain rule should be used, the chain rule is that dy/du*du/dx=dy/dx.

If we say u=(x²+2x) and therefore y=e^u

Then du/dx=2x+2 and dy/du=e^u.

Then dy/du*du/dx= (2x+2)e^u, then we can sub u back into the answer to obtain dy/dx=(2x+2)e^{(x^2+2)}