Question

How do you find the derivative of the function `g(t) = 1/t^(1/2)`?

Answer 1

First, we can rearrange it.

Explanation:

From a power rule, we know that `a^-n=1/a^n`.

Another power rule states that `a^(m/n)=root(n)(a^m)`

Thus, we can rewrite `g(t)=t^(-1/2)`

Now, we simply differentiate it:

`(dg(t))/(dt)=(-1/2)*t^(-3/2)`

`(dg(t))/(dt)=-1/(2t^(3/2))`