Stuck on simple derivative, u(t)*t*e^(-5t), urnt?

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    Derivative Stuck
mr_coffee
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Hello eveyrone, I think my brain just shut down, I'm confused on how i would take the derivative of this function i have circled below:
http://img100.imageshack.us/img100/1671/lastscan2vi.jpg

I know the chain rule, like if it was
t*e^(-5t) = e^(-5t) + t*(-5)e^(-5t)
 
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(u_2 t e^{-7t})' = u_2' t e^{-7t} + u_2 (e^{-7t} + t (-7)e^{-7t})
 
Ahh thank u! I c it now! :biggrin:
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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