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3.5: Derivatives as Rates of Change
https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_1_(Beck)/03%3A_Derivatives/3.05%3A_Derivatives_as_Rates_of_Change
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
3.5: Derivatives as Rates of Change
https://math.libretexts.org/Courses/Laney_College/Math_3A%3A_Calculus_1_(Fall_2022)/03%3A_Derivatives/3.05%3A_Derivatives_as_Rates_of_Change
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
3.5: Rates of Change and Marginal Analysis
https://math.libretexts.org/Courses/Chabot_College/MTH_15%3A_Applied_Calculus_I/03%3A_The_Derivative/3.05%3A_Rates_of_Change_and_Marginal_Analysis
If $f(x)$ is a function defined on an interval $[a,a+h]$ , then the amount of change of $f(x)$ over the interval is the change in the $y$ values of the function over that interval and is given ...If $f(x)$ is a function defined on an interval $[a,a+h]$ , then the amount of change of $f(x)$ over the interval is the change in the $y$ values of the function over that interval and is given by The average rate of change of the function $f$ over that same interval is the ratio of the amount of change over that interval to the corresponding change in the $x$ values.
3.6: Derivatives as Rates of Change
https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT301_Calculus_I/03%3A_Derivatives/3.06%3A_Derivatives_as_Rates_of_Change
If $f(x)$ is a function defined on an interval $[a,a+h]$ , then the amount of change of $f(x)$ over the interval is the change in the $y$ values of the function over that interval and is given ...If $f(x)$ is a function defined on an interval $[a,a+h]$ , then the amount of change of $f(x)$ over the interval is the change in the $y$ values of the function over that interval and is given by The average rate of change of the function $f$ over that same interval is the ratio of the amount of change over that interval to the corresponding change in the $x$ values.
3.4: Derivatives as Rates of Change
https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_1_(Sklar)/03%3A_Derivatives/3.04%3A_Derivatives_as_Rates_of_Change
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
3.5: Derivatives as Rates of Change
https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_(Open_Stax)_Novick/03%3A_Derivatives/3.05%3A_Derivatives_as_Rates_of_Change
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
3.6: Derivatives as Rates of Change
https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Tran)/03%3A_Derivatives/3.06%3A_Derivatives_as_Rates_of_Change
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
3.5: Derivatives as Rates of Change
https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/03%3A_Derivatives/3.05%3A_Derivatives_as_Rates_of_Change
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
3.6E: Exercises for Section 3.6
https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.06%3A_The_Chain_Rule/3.6E%3A_Exercises_for_Section_3.6
This page covers exercises on applying the chain rule for differentiating composite functions and finding derivatives using Leibniz's notation. It includes systematic methods for calculating \(\frac{d...This page covers exercises on applying the chain rule for differentiating composite functions and finding derivatives using Leibniz's notation. It includes systematic methods for calculating $\frac{dy}{dx}$ and finding tangent and normal lines. Additionally, it addresses problems in physics and calculus, emphasizing rates of change in motion, with applications in velocity, acceleration, and geometric changes.
3.6: Derivatives as Rates of Change
https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Nguyen)/03%3A_Derivatives/3.06%3A_Derivatives_as_Rates_of_Change
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
3.5: Derivatives as Rates of Change
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Seeburger)/03%3A_Derivatives/3.05%3A_Derivatives_as_Rates_of_Change
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velo...In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.

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