confused about a quotient rule equation

[pipsy]

f (x) = 5 - xe^x / x + e^x

f'(x) = - (x+e^x) (-xe^x) - (5-xe^x)(1 +e^x)

-----------------------------------------​

(x+e^x)^2
​

f'(x) = - (x+e^x)[-(xe^x + e^x * 1)] - (5+5e^x-xe^x-x^e^2x)

------------------------------------------------------​

(x+e^x)^2
​

What I am confused about is how did (-xe^x) become [-(xe^x+e^x*1)].

Sorry bout the bad formatting, but not sure if this site uses html or w/e for math equations.

 

[Deleted member 4993]

f (x) = (5 - xe^x) / (x + e^x)

Need to use proper grouping symbols () - to preserve order of operations.

f'(x) = - (x+e^x) (-xe^x ) - (5-xe^x)(1 +e^x)

----------------------------------------- ....................... Incorrect ...... should be
​

(x+e^x)^2
​

f'(x) = - (x+e^x) (xe^x + e^x) - (5-xe^x)(1 +e^x)

-----------------------------------------
​

........................(x+e^x)^2


f'(x) = - (x+e^x)[-(xe^x + e^x * 1)] - (5+5e^x-xe^x-x^e^2x)

------------------------------------------------------​

(x+e^x)^2
​

What I am confused about is how did (-xe^x) become [-(xe^x+e^x*1)].

Sorry bout the bad formatting, but not sure if this site uses html or w/e for math equations.

.

The biggest problem of your formatting is that you are not using grouping symbols () to preserve order of operation.

Otherwise your presentation is quite understandable ...

 

[Quaid]

how did [the derivative of] (-xe^x) become [-(xe^x+e^x*1)]

-x*e^x is a product; use the Product Rule, for calculating the derivative of a product.

-x * d/dx[e^x] + e^x * d/dx[-x]

not sure if this site uses html or w/e for math equations

You may use LaTex coding, for pretty math formatting (enclose the coding within [ֺtex] and [/ֺtex] tags), but ASCII text with proper grouping symbols is just fine (as noted by Subhotosh).

I'm not familiar with the abbreviation w/e.

Cheers