## marigirl one year ago Related Rates of change- Differentiation Show that:

1. 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

2. marigirl

$\frac{ dx }{ dt }=v$ Could we state that?

3. baru

hi

4. baru

yes dx/dt is v

5. baru

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

6. 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?

7. baru

do you know the "chain rule" of differentiation?

8. marigirl

oh yup got it! thanks!