## marigirl one year ago Need clarification please Topic: Related rates of change- Differentiation show that: $\frac{ d }{ dx }(\frac{ v^2 }{ 2 })=\frac{ d^2x }{ dt^2 }$ Where x represents the distance travelled in t seconds by a particle moving with velocity v This is what i have so far:

1. marigirl

$\frac{ dx }{ dt }=v$ Differentiate this with respect to time and get $\frac{ d^2x }{ dt^2 }=\frac{ dv }{ dt }$

2. marigirl

we know: $\frac{ dv }{ dt }=\frac{ dv }{ dx }\times \frac{ dx }{ dt }$

3. marigirl

which is $\frac{ dv }{ dt }=\frac{ dv }{ dx } \times v$

4. marigirl

im lost now

5. anonymous

By the chain rule, the left hand side is $\frac{d}{dx}\left[\frac{v^2}{2}\right]=\frac{1}{2}\left(2v\frac{dv}{dx}\right)=v\frac{dv}{dx}$which you showed is equal to $$\dfrac{dv}{dt}$$.

6. marigirl

I am not sure how you for the left side of the equation you wrote above

7. anonymous

Do you know what the chain rule is?

8. marigirl

i think the v and t are confusing me because i keep writing x and y. i might try doing it again