# Derivatives with exponentials!

I have a calculus test that I'm studying for but I've run into some problems! For one, the problem asks to compute the derivative of $f(x)= (1-2x)e^{-x}$. I totally get that $\dfrac{d}{dx}e^{kx}=ke^{kx}$ but i'm not sure where to start in this problem! Help please? thanks!!

• Start with the product rule. – Daniel Fischer Feb 16 '14 at 2:28

Use the product rule. Let $h(x)=1-2x$ and $g(x)=e^{-x}$. Then you'll have $f(x)=h(x)g(x)$. $$f'(x)=h(x)g'(x)+g(x)h'(x)\tag{product rule}$$ Then: $$f'(x)=(1-2x)\cdot\frac{d}{dx}\left(e^{-x}\right)+e^{-x}\cdot\frac{d}{dx}(1-2x)$$