SOLUTION: Differentiate the following function using derivative rule:
f(x)= x^2 e^x
----------- ----------- ---
x^2 + e^x
Algebra.Com
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) =
---------------------------
x^2 + e^x
----
Know this, or get out of the class.
Answer by Boreal(15235) (Show Source): 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.
RELATED QUESTIONS
differentiate the following function using derivative rules :
f(x)=... (answered by Alan3354)
differentiate the following function using derivative rules:
f(x)= (2+ ln... (answered by Boreal)
differentiate the following equation using derivative rules:
f(x)= sqrt(x)... (answered by Alan3354)
differentiate the following function
f(x)=... (answered by rothauserc,Edwin McCravy)
differentiate the following function:
(a)f(x)=(x^2+1/x^3 )(x^3-x^2+1)
(b)f(x)=... (answered by Edwin McCravy)
differentiate the following function:
f(x)=(x^2+1/x^3 )(x^3-x^2+1)
f(x)=... (answered by solver91311)
differentiate the following function:
f(x)=(x^2+1/x^3 )(x^3-x^2+1)
(answered by Edwin McCravy)
differentiate the following function:
f(x)=(x^2+1/x^3 )(x^3-x^2+1)
(answered by Alan3354)
differentiate the following function:
f(x)=(x^2+1/x^3... (answered by rothauserc)