marigirl
  • marigirl
Related Rates of change- Differentiation Show that:
Mathematics
chestercat
  • chestercat
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marigirl
  • marigirl
Show that: \[\frac{ d }{ dx }(\frac{ v^2 }{ 2 })=\frac{ d^2x }{ dt^2 } \] Where x represents the distance traveled in t secs by a particle moving with velocity v
marigirl
  • marigirl
\[\frac{ dx }{ dt }=v\] Could we state that?
baru
  • baru
hi

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baru
  • baru
yes dx/dt is v
baru
  • baru
differentiate dx/dt=v again with respect to time to get \[d^2x/dt^2=dv/dt\]
baru
  • baru
now you can replace the right hand side of the given equation with "dv/dt". now all thats left to do, is to show that the left hand side of the equation some how reduces to dv/dt. with me so far?
baru
  • baru
do you know the "chain rule" of differentiation?
marigirl
  • marigirl
oh yup got it! thanks!

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