Another difficulty with differentiation

[jonnburton]

I'm not sure whether the mistake is mine or whether there might be an error in the book with this. I've gone over this and differentiated it several times and always come to the same answer, which is different to that given in the book.

Could anyone take a look at this and tell me if I'm making a mistake?

A curve has the equation \(\displaystyle (x+2)e^{-x}\)

The point p has x-coordinate 3. Find \(\displaystyle \frac{dy}{dx}\) at point P, leaving your answer in terms of e.

\(\displaystyle \frac{dy}{dx} (x+2)e^{-x} = -(x+2)e^{-x} + 2e^{-x}\)

Putting in the value of x gives:

\(\displaystyle -(3+2)e^{-3}+2e^{-3} = -5e^{-3}+2e^{-3} = -3e^{-3}\)

However, the answer the book gives is \(\displaystyle -4e^{-3}\)

Thanks

 

[MarkFL]

In your application of the product rule, you have incorrectly stated that:

\(\displaystyle \dfrac{d}{dx}(x+2)=2\)

 

[jonnburton]

Ah, thank you MarkFL... I think I've managed to sort it after paying attention to that.