How To Solve Derivative Problems

In this page we'll first learn the intuition for the chain rule.

This intuition is almost never presented in any textbook or calculus course.

If you have a problem, or set of problems you can't solve, please send me your attempt of a solution along with your question.

In this case, the question that remains is: where we should evaluate the derivatives?

Let's rewrite the chain rule using another notation. According to the rule, if: So, as you can see, the chain rule can be used even when we have the composition of more than two functions.

This rule says that for a composite function: As I said, it is useful for this type of comosite functions to think of an outer function and an inner function. In the previous examples we solved the derivatives in a rigorous manner. Solving derivatives like this you'll rarely make a mistake. In fact, this faster method is how the chain rule is usually applied. We had: If you have just a general doubt about a concept, I'll try to help you.

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.

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