1. ## Differentiation

A particle is moving along a curve given by y= (t^(3)+1)^(1/2). Determine the acceleration when t=2 seconds.

I know the first derivative is 3t^(2)/2*((t^(3)+1)^(1/2))?? The second derivative will give me acceleration.

Please help with the second derivative and tell me if my first derivative is correct.

2. $y = \sqrt{t^3 + 1}$

$\Longrightarrow$
$\dot{y} = \frac{3 t^2}{2 \sqrt{t^3+1}}$ by chain rule.

$\Longrightarrow$
$\ddot{y} = \frac{3t}{(t^3+1)^{\frac{1}{2}}} - \frac{9t^4}{4(t^3+1)^{\frac{3}{2}}}$ by product rule.