Find the second order derivative of y=9 log t3.a)27/t2b)-(27/t2)c)-(1/t2)d)-(27/2t2)Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Finding the second order derivative of a given function involves differentiating it twice with respect to the independent variable. In this case, we need to find the second order derivative of the function y = 9 log(t^3).

To find the second order derivative, we follow these steps:

First Order Derivative:
- Differentiate the function y = 9 log(t^3) with respect to t using the chain rule.
- The derivative of log(t^3) is 3/t.
- Multiply this by the derivative of 9, which is 0.
- So, the first order derivative of y is dy/dt = (27/t).

Second Order Derivative:
- Now, differentiate the first order derivative (dy/dt) with respect to t.
- The derivative of (27/t) is -27/t^2.
- Therefore, the second order derivative of y is d²y/dt² = -(27/t^2).

According to the options provided, the correct answer is option 'B', which states that the second order derivative is -(27/t^2).

In summary:
- The first order derivative of y = 9 log(t^3) is dy/dt = (27/t).
- The second order derivative of y = 9 log(t^3) is d²y/dt² = -(27/t^2).

Answer

Given that, y=9 log⁡t³

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