- #1
MacLaddy
Gold Member
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Homework Statement
Compute the derivative of the following function
[itex](1-2x)e^{-x}[/itex]
Homework Equations
Product Rule and Quotient rule
The Attempt at a Solution
My problem here is that I come up with two different answers when I use the quotient rule vs. the product rule.
Trying it with the product rule
f(x)= (1-2x)e^-x
f'(x)= -2e^-x + e^-x(1-2x)
f'(x)= e^-x(-2+(1-2x))
[itex]f'(x)= e^{-x}(-1-2x)[/itex] or [itex]\frac{-1-2x}{e^x}[/itex]
With the quotient rule
f'(x)= (e^-x(1-2x) - (-2e^-x)) / [e^-x]^2
f'(x)= (e^-x-2e^-x+2e^-x) / [e^-x]^2
f'(x)= (e^-x(-2x+2)) / [e^-x]^2
[itex]f'(x)= \frac{-2x+2}{e^{-x}}[/itex] or [itex]e^x(-2x+2))[/itex]
As you can see, these are two different answers. I would think that I should have the same solution either way I do this, so what am I doing wrong?
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