+0  
 
-1
115
2
avatar+27 

What is the derivative of this function?
\(g(t) = (t^3+3t^2+t)/(t^3)\)

I'm not getting how the extended power rule works
Thanks for any help

CurlyFry  Mar 26, 2018
 #1
avatar+9433 
+3

What is the derivative of this function?

laugh

Omi67  Mar 26, 2018
 #2
avatar+19475 
+3

What is the derivative of this function?

\(g(t) = (t^3+3t^2+t)/(t^3)\)

g(t) = (t^3+3t^2+t)/(t^3)

I'm not getting how the extended power rule works

 

Formula power rule:

\(\begin{array}{|rcll|} \hline f(x) &=& x^n,\quad n \ne 0 \\ f'(x) &=& n\cdot x^{n-1} \\ \hline \end{array} \)

 

\(\begin{array}{|rcll|} \hline g(t) &=& \dfrac{t^3+3t^2+t} {t^3} \\\\ &=& \dfrac{t^3} {t^3} +\dfrac{3t^2} {t^3}+\dfrac{t} {t^3} \\\\ &=& 1 + 3\cdot t^{2-3} + t^{1-3} \\\\ &=& 1 + 3\cdot t^{-1} + t^{-2} \quad & | \quad \text{power rule} \\\\ g'(x) &=& 0 + 3\cdot \left((-1)\cdot t^{-1-1} \right)+ (-2) \cdot t^{-2-1} \\\\ &=& -3\cdot t^{-2} - 2 \cdot t^{-3} \\\\ &=& - \dfrac{3}{t^2} - \dfrac{2}{t^3} \\\\ \hline \end{array} \)

 

laugh

heureka  Mar 26, 2018

8 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.