B What Is the Meaning of $\frac{d}{dx} \frac{dy}{dx}$?

[askor]

Can someone please tell me what is meant by $\frac{d}{dx} \frac{dy}{dx})$?

 

[Doc Al]

That's the 2nd derivative of y with respect to x.

 

[askor]

If $y = t^2$ and $x = t$, what is its $\frac{d}{dx} (\frac{dy}{dx})$?

I know that $\frac{dy}{dx} = \frac{2t}{1} = 2t$.

 

[Doc Al]

You can rewrite $y = t^2$ as $y = x^2$. Then $\frac{dy}{dx} = 2x$.

Take the next derivative of that.

 

[askor]

What about, if, $y = t^2 +2t + 1$ and $x = t$, what is its 2nd derivative?

 

[Doc Al]

Same idea. Rewrite it in terms of x and take the derivatives.

 

[sysprog]

It looks like acceleration to me $-$ 2nd derivative of position with respect to time, the 1st being velocity, the 3rd being jerk, the 4th, jounce or snap (jounce being by some called snap at least partly so that some whimsical people can wryly call the 4th, 5th, and 6th, snap crackle, and pop, respectively.

 

[askor]

Same idea. Rewrite it in terms of x and take the derivatives.

Can you show in terms of t (parametric)? I know that $\frac{dy}{dx} = \frac{dy}{dt}/\frac{dx}{dt}$.

 

[Doc Al]

Just use t as the variable and take derivatives with respect to t.

 

[askor]

Can you show in form of t (parametric)? I know that $\frac{dy}{dx} = \frac{dy}{dt}/\frac{dx}{dt}$.

 

[Doc Al]

Have a look at this: Parametric derivative