Derivative of exponential function
Elements of Calculus with Applications
1.3 Use a limit to find the derivative of a function. 1.4 Tell if a function is continuous at given values of x. Find derivatives of algebraic, logarithmic, and exponential functions, and use derivatives to solve applied problems and produce graphs. 2.1 Use the quotient rule to find the derivative of a function.
[DOC File]Developing an Intuitive Grasp of Exponential Functions ...
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Albert A. Bartlett (1976) stated “The greatest shortcoming of the human race is our inability to understand the exponential function” (p.394). It is unsurprising that many of our high school students have difficulty grasping concepts involving exponentials (Weber, 2002).
[DOC File]Section 1 - Radford University
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When taking the derivative of the second function, we apply the chain rule applied to the exponential function of base e. This gives Chain Rule. Used to take the derivative of a composition of two functions. Chain Rule. Note: The general power rule and chain rule for the exponential function are special cases of the Chain Rule. Example 9:
[DOC File]Section 1
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When taking the derivative of the second function, we apply the chain rule applied to the exponential function of base e. This gives Chain Rule. Used to take the derivative of a composition of two functions. Chain Rule. Note: The general power rule and chain rule for the exponential function are special cases of the Chain Rule. Example 9:
[DOC File]Simple Rules for Differentiation
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Exponential Functions. The natural exponential function is a function that has a very special property (see Sydsaeter text for proof) that for the function , (the derivative of the function is the function itself). For a general exponential function , . Remember here a is a …
[DOC File]Derivatives - UH
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Well the derivative of the graph is approximately. For one tiny step sideways at 2 the y value goes up 230. That’s pretty steep, folks. This is a pattern for the exponential functions: Only escapes that multiplier because ! So the derivative of an exponential is a specific, dependable multiple of …
[DOC File]Exponential and Logarithmic Derivatives Worksheet
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Supplemental Instruction. Math 151. This worksheet is arranged in order of increasing difficulty. For problems 1-8, find the derivative of the given function:
[DOC File]AP CALCULUS AB
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DERIVATIVES OF POLYNOMIALS AND EXPONENTIAL FUNCTIONS. Derivative of a Constant Function. Suppose we have a function . Graph the function: The slope of a tangent line to any point on the graph would be _____. So: Power Functions. Now, let’s look at functions that take the form , where n is a positive integer.
[DOC File]Unit 6: Exponential and Logarithmic Functions
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As we expected, the exponential function is smaller than the exponential function . So what happens if the starting value of is negative? Let’s find out. Example 3. Graph the exponential function . Solution. Let’s make a table of values: -2 -1 0 -5 1 -10 2 -20 3 -40 Now let's graph the function: This result shouldn’t be unexpected.
[DOC File]Inverse Functions
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Thus the derivative of an exponential function is . In the special case where the base is since the derivative rule becomes . To generalize, if is a differentiable function of with the use of the Chain Rule the above derivatives take the general form . And if . Derivatives of Exponential Functions. Example 9: Find the derivative of . Solution ...
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