# The tip of a fishing pole is located 10 feet above the water. This is kept constant as a fish is...

## Question:

The tip of a fishing pole is located 10 feet above the water. This is kept constant as a fish is reeled in. The fish is reeled in so that its rate of change in the horizontal direction is 1.5 feet per second. At what rate is the angle between the fishing line and the water changing when there is a total of 12.5 feet of fishing line out?

## Application of Derivatives:

The computation of derivatives is required in many problems to estimate the equation's solution where the rate of change of any quantity needs to be found out. For example, if the function is {eq}y = f\left( x \right) {/eq} then, to find the derivative of {eq}y {/eq} with respect to time leads to chain rule such as {eq}\dfrac{{dy}}{{dt}} = \dfrac{{dy}}{{dx}} \cdot \dfrac{{dx}}{{dt}} {/eq}.

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Given data

• The length of the fishing pole above the water is {eq}d = 10\;{\rm{ft}} {/eq}.
• The decreasing rate of change of the fish reel is...

The Chain Rule for Partial Derivatives

from

Chapter 14 / Lesson 4
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When evaluating the derivative of composite functions of several variables, the chain rule for partial derivatives is often used. In this lesson, we use examples to explore this method.