Is this correct take the derivative of

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The discussion revolves around the differentiation of the expression (t-1)^(1/2) * (t^-2) using the product rule. One participant confirms their derivative calculation, arriving at (t-1)^(-1/2) * t^(-3) * (-3/2t + 2). Another participant expresses confusion about the steps leading to a specific term in the derivative, particularly regarding the factorization used. The conversation highlights the complexities of applying the product rule and the importance of clarity in mathematical communication. Overall, the participants engage in verifying and clarifying their derivative calculations.
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(t-1)^1/2*(t^-2)

I hope you guys can understand what I am trying to say up there... SO i did the product rule, and my answer was this.. lemmi know if it's correct...thanks a bunch.

(t-1)^-1/2 t^-3 { -3/2t +2 }

That was my answer...
 
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I get

\frac{1}{2}\left[(t-1)^{-\frac{1}{2}}\right] t^{-3} \left(4-3t\right)

Which is the same thing,so everything is okay. :smile:

Daniel.

P.S.Lakers missed the play-offs :wink:
 
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hey that looks perfect to me!
 
is this what you trying to differentiate - (t-1)^{\frac{t^2}{2}} or is this
(t-1)^{\frac{1}{2}} \frac{t^2}{2}
 
Nope.

(t-1)^{\frac{1}{2}} t^{-2}

Daniel.
 
dextercioby said:
Nope.

(t-1)^{\frac{1}{2}} t^{-2}

Daniel.
I can see where the \frac{1}{2}\left[(t-1)^{-\frac{1}{2}}\right] came from but the t^{-3} \left(4-3t\right) has lost me. What did you do to get that because I would have just done -2t^{-3}

The Bob (2004 ©)
 
I forced something as a factor (v.above),and that's how i ended up with that paranthesis.

Daniel.
 

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