## anonymous 4 years ago Find y'(x) Given y(x)=5-2(x+1)e^-1/2x (x is bigger or equal to 0)

1. lalaly

$y=5-2(x+1)e^{\frac{-1}{2}x}$ is this the function?

2. anonymous

3. anonymous

using the product rule,i can go as far as ; -2(e^-1\2x)+5-2(x+1)(-1/2e^-1/2x) the answer is (x-1)e^-1/2x. my problem is i cant figure out how they got to the answer? CAN ANYONE HELP!

4. lalaly

yeah i will do it

5. lalaly

$y=5-2xe^{-\frac{1}{2}x}-2e^{-\frac{1}{2}x}$$y'=-2e^{-\frac{1}{2}x}+(-2xe^{-\frac{1}{2}x} \times \frac{-1}{2})+e^{-\frac{1}{2}x}$$=-2e^{-\frac{1}{2}x}+xe^{-\frac{1}{2}x}+e^{-\frac{1}{2}x}$$=-e^{-\frac{1}{2}x}+xe^{-\frac{1}{2}x}$now factor out the e^(1/2)x $=e^{-\frac{1}{2}x}(-1+x)$$=(x-1)e^{-\frac{1}{2}x}$