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Math Help - Differentiation

  1. #1
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    Smile 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.
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  2. #2
    Junior Member
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    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.
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