Find the derivative of F(x) = x^2(e^x) + e^x

[Ashley5]

Find the derivative

F(x) = x^2(e^x) + e^x
f'(x) = x^2(e^x) + e^x(x^2) + e^x
f'(x) = X^2(e^x) +e^x(2x) + e^x

Is this right? I'm a little confused, how do you get to this point on the formula/rule? Thank you!

 

[pka]

FACTOR.
\(\displaystyle \L\begin{array}{l} y = x^2 e^x + e^x = e^x \left( {x^2 + 1} \right) \\
y' = e^x \left( {x^2 + 1} \right) + \left( {e^x } \right)\left( {2x} \right) \\
\end{array}\)

Now you simplify and continue.

 

[o_O]

Well your answer is right. Just that you forgot to the primes (the " ' " marks) on the second line:

f'(x) = x²(e^x)' + e^x(x²)' + e^x

Assuming you meant the primes to go where the brackets are. You could always simplify your final answer.

 

[pka]

Well your answer is right. Just that you forgot to the primes (the " ' " marks) on the second line:
f'(x) = x²(e^x)' + e^x(x²)' + e^x
Assuming you meant the primes to go where the brackets are. You could always simplify your final answer.

What are you on about?
There is nothing correct about that answer.
No one uses primes in an answer of this kind.
Where have you been?

 

[o_O]

The OP says to find the derivative of f(x) = x²e^x + e^x. Use the product rule for the first term, which is what the OP did but without the notation, and the just simply take the derivative of the second term which is what he/she did as well. Unless I'm misreading something ...

Your advice on factoring out the e^x comes to the same answer too.