Find the derivative of the function.
y = x^2 e^x − 2xe^x + 4e^x
y'=

Question

Find the derivative of the function.
y = x^2 e^x − 2xe^x + 4e^x
y'=

zepdrix · Answer

Mmm you might wanna factor an e^x out of each term before taking the derivative. Might make it a smidge easier.

zepdrix · Answer

$$\large y = e^x(x^2−2x+4)$$

zepdrix · Answer

Here is the product rule, let's try to setup our derivative using this rule.$$\large (uv)'=\color{royalblue}{u'}v+u\color{royalblue}{v'}$$

$$\large y'=\color{royalblue}{(e^x)'}(x^2−2x+4)+e^x\color{royalblue}{(x^2−2x+4)'}$$The blue terms we will need to differentiate.
Understand the setup?

anonymous · Answer

yes

zepdrix · Answer

Hmmm so what do you get for your derivatives? c:
How 'bout the first one?

derivative of e^x? :O

anonymous · Answer

2x-2

zepdrix · Answer

$$\large y'=\color{royalblue}{(e^x)'}(x^2−2x+4)+e^x\color{orangered}{(2x−2)}$$
For the second one? Yah looks good!

anonymous · Answer

lol @zepdrix it really look good :)

zepdrix · Answer

heh yah, i love the colors ^^