Question

How to find the derivative of the following function: f(t)= 1/ 2t^3? Thank you

Answer 1

`f'(t) = -3/(2t^4)`

Explanation:

`f(t) = 1/(2t^3)`.

Since `a^-b = 1/a^b`, we can rewrite `1/t^3 = t^-3`

`f(t) = 1/2t^-3`.

Using the power rule, which states that `(x^n)' = nx^(n-1)`, we get:

`f'(t) = 1/2 * (t^-3)' = 1/2 * (-3t^-4) = -3/2t^-4 = -3/(2t^4)`