so i am having trouble finding the answer

h't if h(t)= 5/t^1/4 - 6/t^2/3

In google type calc101

When you see list of results click on:
calc101com

When page be open click option: derivatives

When page be open in rectacangle type:

5/(t)^(1/4)-6/(t)^(2/3)

In rectacangle:
with respect to type t

In rectacangle:
and again with respect to type t

Then click options DO IT

You will see solutions step-by-step

5/t^1/4 - 6/t^2/3

I rewrite as, (my preference)
5t^(-1/4) - 6t(-2/3)

h' =
-1/4 * 5t^(-5/4) - (-2/3 * 6t^(-5/3))
h' = -5/4t^(-5/4) + 12/3t(-5/3)
h' -5/4t^(-5/4) + 4t(-5/3)
h' = 4/(t^(5/3)) - 5/(t(^5/4))

You also can in google type:

derivatives online

When you see listo of results click on:

numberempirecom/derivatives.php

and

solvemymathcom/online_math_calculator/calculus/derivative_calculator/index.php

On this sites you will see your derivation in two different simplify forms

To find the value of h(t) for a specific value of t, you need to substitute that value into the equation for h(t). Let's say you want to find the value of h(t) when t = 2. First, you'll substitute 2 in place of t in the equation:

h(t) = 5/t^(1/4) - 6/t^(2/3)

h(2) = 5/2^(1/4) - 6/2^(2/3)

Next, simplify the equation:

h(2) = 5/√2 - 6/2^(2/3)

To simplify further, you can express 2^(1/4) as the fourth root of 2, and 2^(2/3) as the cube root of 2 squared:

h(2) = 5/√2 - 6/(2^(2/3))
= 5/2^(1/4) - 6/(2^(2/3))
= 5/(√2) - 6/∛(2^2)

Now, you can calculate the numerical value of h(2) using a calculator to evaluate the square root and cube root:

h(2) ≈ 5/1.414 - 6/1.587
≈ 3.54 - 3.78
≈ -0.24

Therefore, h(2) is approximately -0.24. You can follow a similar process to find the value of h(t) for any other value of t.