Question

Related Rates of change- Differentiation
Show that:

Answer 1

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

Answer 2

\[\frac{ dx }{ dt }=v\]

Could we state that?

Answer 3

hi

Answer 4

yes dx/dt is v

Answer 5

differentiate dx/dt=v again with respect to time to get
\[d^2x/dt^2=dv/dt\]

Answer 6

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?

Answer 7

do you know the "chain rule" of differentiation?

Answer 8

oh yup got it! thanks!