SOLUTION: Differentiate the following function using derivative rule:
f(x)= x^2 e^x
----------- ----------- ---
x^2 + e^x
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-> SOLUTION: Differentiate the following function using derivative rule:
f(x)= x^2 e^x
----------- ----------- ---
x^2 + e^x
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Question 1051081: Differentiate the following function using derivative rule:
f(x)= x^2 e^x
---------------------------
x^2 + e^x Found 2 solutions by Alan3354, Boreal:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Differentiate the following function using derivative rule:
f(x)= x^2 e^x
f'(x) =
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x^2 + e^x
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Know this, or get out of the class.
You can put this solution on YOUR website! (x^2*e^x)/(x^2+e^x)
The derivative will have the above denominator squared as the denominator.
The result will be (x^2+e^x)(2x*e^x+x^2*e^x)-(x^2*e^x)(2x+e^x)/[x^2+e^x)^2]
If you multiply the numerator out, it is 2x^3*e^x+x^4*e^x+2x*e^2x+x^2*e^2x-
2x^3*e^x-x^2*e^2x.
The 2x^3*e^x and x^2*e^2x cancel
The answer can be written as (x^4*e^x+2x*e^2x)/(x^2+e^x)^2.
