Question

How do you differentiate `f(x)=e^(-2x^2+x+1)` using the chain rule?

Answer 1

I found: `f'(x)=(1-4x)e^(-2x^2+x+1)`

Explanation:

Here you first derive the exponential as it is (red) and then multiply by the derivative of the exponent (blue):
`f'(x)=color(red)(e^(-2x^2+x+1))*(color(blue)(-4x+1))`

Basically with the Chain Rule you use the same technique as in the Matrioska Dolls (one doll inside the other). You derive the "big" function (the exponential in this case) and once you "opened" it you derive the one inside it (the exponent).