Second Deriv

[lislr8]

Hi,

Can someone explain what the difference is between taking the second derivative and taking the derivative of something twice?

i.e. IF x=t^2 and y= (t^3)-3t

dy/dx = (3t^2-3)/(2t)

However, d^2y/dx^2 = 3(t^2+1)/4t^3, basically in the example in the book it says take d/dt (dy/dx)and divide it by dx/dt

and if I just took the derivative of dy/dx again using quotient rule I get 3(t^2+1)/(2t^2)

Thanks for your help,
lislr8

 

[skeeter]

\(\displaystyle \frac{d}{dx}\left(\frac{3t^2 - 3}{2t}\right) =\)

note the use of the chain rule ...

\(\displaystyle \frac{2t \cdot 6t \cdot \frac{dt}{dx} - (3t^2 - 3) \cdot 2 \frac{dt}{dx}}{(2t)^2} =\)

\(\displaystyle \frac{\frac{dt}{dx}[12t^2 - (6t^2 - 6)]}{(2t)^2} =\)

\(\displaystyle \frac{6t^2 + 6}{(2t)^2 \cdot \frac{dx}{dt}} =\)

\(\displaystyle \frac{6t^2 + 6}{(2t)^3} =\)

\(\displaystyle \frac{6(t^2 + 1)}{8t^3} = \frac{3(t^2+1)}{4t^3}\)