Question

What is the derivative of #y= -e^(x^2+x-3) #?

Answer 1

`-(2x+1)e^(x^2+x-3)`

Explanation:

According to the Chain Rule, the derivative of `e^u` is equivalent to `u'e^u`.

So, we can say that `y'=-(d)/(dx)[x^2+x-3]*e^(x^2+x-3)`.

We can calculate that `d/(dx)[x^2+x-3]=2x+1`.

Now, we plug the value of the derivative back into the equation we found from the chain rule to determine that `color(red)(y'=-(2x+1)e^(x^2+x-3)`