How to differentiate the following functions with respect to t and simplify where possible....
S supra New member Joined Mar 28, 2006 Messages 2 Mar 30, 2006 #1 How to differentiate the following functions with respect to t and simplify where possible....
tkhunny Moderator Staff member Joined Apr 12, 2005 Messages 11,339 Mar 30, 2006 #2 Why are you struggling with these? It's just a bunch of constants. Break out you Chain Rule and give it a go. f(t) = (1−β∗t)−α\displaystyle f(t)\,=\,(1-\beta*t)^{-\alpha}f(t)=(1−β∗t)−α dfdt = −α∗(1−β∗t)−α−1∗(−β) = αβ∗(1−β∗t)−(α+1)\displaystyle \frac{df}{dt}\,=\,-\alpha*(1-\beta*t)^{-\alpha-1}*(-\beta)\,=\,\alpha\beta*(1-\beta*t)^{-(\alpha+1)}dtdf=−α∗(1−β∗t)−α−1∗(−β)=αβ∗(1−β∗t)−(α+1) You do the other one and show us what you get.
Why are you struggling with these? It's just a bunch of constants. Break out you Chain Rule and give it a go. f(t) = (1−β∗t)−α\displaystyle f(t)\,=\,(1-\beta*t)^{-\alpha}f(t)=(1−β∗t)−α dfdt = −α∗(1−β∗t)−α−1∗(−β) = αβ∗(1−β∗t)−(α+1)\displaystyle \frac{df}{dt}\,=\,-\alpha*(1-\beta*t)^{-\alpha-1}*(-\beta)\,=\,\alpha\beta*(1-\beta*t)^{-(\alpha+1)}dtdf=−α∗(1−β∗t)−α−1∗(−β)=αβ∗(1−β∗t)−(α+1) You do the other one and show us what you get.
