The population of a herd of deer is modeled by P(t) = 1000 + 500 \sin \Big( 2 \pi t -...
Question:
The population of a herd of deer is modeled by {eq}P(t) = 1000 + 500 \sin \Big( 2 \pi t - \frac{\pi}{2} \Big ) {/eq}, where t is measured in years from January 1. Estimate roughly how fast the population is changing on the first of July.
Chain Rule
When we have an expression inside of another expression, which is called a composition of functions, we need to apply the Chain Rule to find the derivative of it. This useful technique states that {eq}(f \circ g)'(x) = f'(g(x)) g'(x) {/eq}.
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View this answerIn order to find how the population is changing at any time, we need to find the derivative of this function. Since we have a linear expression inside...
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