Math Help - Doubts about derivatives

I started to learn calculus following a book but I don’t understand the explanation of a derivative example. Here is the excerpt of the book:

Then the Pythagorean theorem tells us that

h(t)^2 + b(t)^2 = 13^2

We may differentiate both sides of this equation with respect to the variable t
(which is time in minutes) to obtain

2 · h(t) · h(t) + 2 · b(t) · b(t) = 0

It seems that the author applied the Chain Rule but I am not sure about the intermediary steps of this differentiation. Could someone show me the intermediary steps and explain them if needed ?

2. Originally Posted by tedhill
I started to learn calculus following a book but I don’t understand the explanation of a derivative example. Here is the excerpt of the book:

Then the Pythagorean theorem tells us that

h(t)^2 + b(t)^2 = 13^2

We may differentiate both sides of this equation with respect to the variable t
(which is time in minutes) to obtain

2 · h(t) · h(t) + 2 · b(t) · b(t) = 0

It seems that the author applied the Chain Rule but I am not sure about the intermediary steps of this differentiation. Could someone show me the intermediary steps and explain them if needed ?
We have,
$h^2(t)+b^2(t) = 13^2$
Now,
$h^2(t)$ can be thought of (mentally) as $H(u) = u^2 \mbox{ where }u=h(t)$
So,
$\frac{d [ h^2(t)]}{dt} = \frac{dH}{du}\cdot \frac{du}{dx}=2u \cdot h'(t) = 2h'(t)h(t)$

Similary with $b^2(t)$.

3. Thank you, ThePerfectHacker.