SOLUTION: find the derivative f(x)=x^4*e^3x f'(x)= this is what I came up with and it says my answer is wrong- what did I do wrong f'(x) 4x^3*e^3x*3

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: find the derivative f(x)=x^4*e^3x f'(x)= this is what I came up with and it says my answer is wrong- what did I do wrong f'(x) 4x^3*e^3x*3       Log On


   

Question 202798: find the derivative
f(x)=x^4*e^3x
f'(x)=
this is what I came up with and it says my answer is wrong- what did I do wrong
f'(x) 4x^3*e^3x*3
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the derivative
f(x)=x^4*e^3x
f'(x)=
this is what I came up with and it says my answer is wrong- what did I do wrong
f'(x) 4x^3*e^3x*3
---------------
It's a product, so you have to follow the product rule.
f'(x) = x^4 + [e^(3x)*12x^2]
Then simplify.
=========================
Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I was working on this problem when I noticed that Stanbon got to it first, but after looking at his solution, I don't quite understand how he arrived at what he got! So here's my take on it.
Find the derivative of:
f%28x%29+=+x%5E4%2Ae%5E%283x%29
Since you are asked to find the derivative of a product of two functions of x, you will need to use the following rules of differential calculus:
d%28u%2Av%29%2Fdx+=+u%2A%28dv%2Fdx%29+%2B+v%2A%28du%2Fdx%29 also:
d%28e%5Em%29%2Fdx+=+e%5Em%2A%28dm%2Fdx%29 Note: u, v, and m are all functions of x.
So here we go:

d%28f%28x%29%29%2Fdx+=+x%5E4%2Ae%5E%283x%29%2A3+%2B+e%5E%283x%29%2A4x%5E3 Factor out e%5E%283x%29
highlight%28d%28f%28x%29%29+=+e%5E%283x%29%283x%5E4%2B4x%5E3%29%29