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And if the rate at which temperature drops with height changes with the height you're at (if you're higher the drop rate is faster), T'(h) changes with the height h.
The chain rule is one of the essential differentiation rules.
It allows us to calculate the derivative of most interesting functions.
After we've satisfied our intuition, we'll get to the "dirty work".
We'll learn the step-by-step technique for applying the chain rule to the solution of derivative problems.
It would be the rate at which temperature changes with time at that specific height, times the rate of change of height with respect to time.
That is: This makes perfect intuitive sense: the rates we should consider are the rates at the specified instant.
The chain rule is a formula to calculate the derivative of a composition of functions.
Once you have a grasp of the basic idea behind the chain rule, the next step is to try your hand at some examples. Use the chain rule to calculate $h'(x)$, where $h(x)=f(g(x))$.
So, what we want is: because the dh "cancel out" in the right side of the equation.
Notice that the second factor in the right side is the rate of change of height with respect to time.