1. A submarine is 40 meters below sea level. It goes up 12 meters, then goes down 30 meters. What is the submarine's new positio
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Answer:
The inner function is and the outer function is
.
The derivative of the function is .
Step-by-step explanation:
A composite function can be written as , where
and
are basic functions.
For the function .
The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.
Here, we have inside parentheses. So
is the inner function and the outer function is
.
The chain rule says:
It tells us how to differentiate composite functions.
The function is the composition,
, of
outside function:
inside function:
The derivative of this is computed as
The derivative of the function is .