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.