Use the power rule to compute the derivative d/dt * t^2/3 for t=4?

Question

Use the power rule to compute the derivative d/dt * t^2/3 for t=4?

Answer 1

The power rule is this:

Derivative of x^a (with respect to x) is ax^(a-1)

So, ∂t^(2/3)/∂t is (2/3)t^(-1/3), or 2÷(3∛t)

We evaluate at 4 by setting t to 4 and stopping there for math, or working it out in a calculator for science/engineering.