Step 1:

First, we will remove the fractions, by rewriting the function as follows:

[latex]\large{h'(x) = h^{-2} + 3h^{-3}}[/latex]

Notice that we can now use the derivative power rule to find the derivative.

Step 2:

Applying the power rule, we have:

[latex]\large{h'(x) = (-2)h^{-2-1} + 3(-3)h^{-3-1}}[/latex]

[latex]\large{h'(x) = -2h^{-3}\: -\: 9h^{-4}}[/latex]

Notice how we brought the exponent down and subtracted the exponent by 1.

Thus, we have:

[latex]\large{h'(x) = -\frac{2}{h^3}\: -\: \frac{9}{h^4}}[/latex]

This is our final answer for the derivative.

Solution Complete!