1. ## differentiate 8te^-t

how do you differentiate 8te^-t
i tried to put it into one of them differential calculators but i cant understand the steps.

this is how i thought if would work

using the product rule 8t*e^-t-1 +e^-t*8 i dont think this is the right answer

2. ## Re: differentiate 8te^-t

$\dfrac{d}{dt}\left( 8te^{-t}\right) = 8t \cdot \left[e^{-t} \cdot (-1)\right] + e^{-t} \cdot 8 = -8te^{-t} + 8e^{-t} = 8e^{-t}(1-t)$

When are you going to learn how to post up using Latex?

3. ## Re: differentiate 8te^-t

soon is there a link i could follow to do it?i see what i was doing wrong. i was treating e^-x wrong

4. ## Re: differentiate 8te^-t

Originally Posted by markosheehan
soon is there a link i could follow to do it?i see what i was doing wrong. i was treating e^-x wrong
Why not just learn the product rule? $\large{(f\cdot g)'=(f'\cdot g)+(f\cdot g')}$

5. ## Re: differentiate 8te^-t

Originally Posted by markosheehan
soon is there a link i could follow to do it?i see what i was doing wrong. i was treating e^-x wrong
There is an entire forum on this site devoted to it ...

LaTeX Help

6. ## Re: differentiate 8te^-t

Originally Posted by markosheehan
soon is there a link i could follow to do it?i see what i was doing wrong. i was treating e^-x wrong
Yes, you are treating "$\displaystyle e^t$" as if it were "$\displaystyle t^e$". The derivative of $\displaystyle t^e$, with respect to t is $\displaystyle et^{e- 1}$ but the derivative of $\displaystyle e^t$ is $\displaystyle e^t$.