Questions tagged [derivative]
The derivative tag has no usage guidance.
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A visualization for the quotient rule
Context: first year didactics of mathematics course for middle school teacher students (in Norway).
I have a reasonable visualization for the product rule of derivatives: Consider a rectangle with ...
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Interpreting the derivative as instantaneous rate of change in real phenomena
When interpreting the meaning of the derivative in real phenomena, it may seem that the interpretation is in conflict with the definition of the derivative itself. The confusion is caused by the units ...
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What are some examples of great functions that are not too elementary (easy)?
I am teaching precalculus/basic calculus to my class (high schoolers of around 18 years of age), and I'm always searching for nice functions to plot and study (finding the domain, the function's sign, ...
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Do we need to practice equation derivation while learning math if equations will be chunked and automatized?
When I was learning the Pythagorean theorem(at time A), I was just told to memorize it. I used it often before trying to derive the equation(at time B), and I think actually I have forgotten the ...
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Good Examples of Equations Derived from Elementary Calculus
I'm collecting additional enrichment content for my calculus students. I'm looking for examples of equations that are used in various fields, but which can be derived at least somewhat ...
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Good exercises that force you to apply the definition of the derivative, without explicitly telling you to do so?
I'd like to ask my students whether some real function is differentiable at a certain $x_0$. I prefer not telling them that they have to use the definition of the derivative, but to instead present a ...
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Exponential & logarithm in a high school calculus class
So recently I was teaching high school calculus to a high school class and I was wondering about the pedagogically best way to make students actually understand why the derivatives of the exponential &...
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How does one tutor an A-level student past the derivative paradox?
EDIT (two years later): I was saddened to realise that no-one seems to care at the school level. Everything I thought might be a problem ended up as a non-issue because no-one challenged anything. The ...
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Locus of the maximal turning point and the point of inflection
Suppose you have a carton that has the form of a square with sides of length a. If we want to produce a box out of it whose height is x we might deduce the following formula:
$$V_a(x)= x(a-2x)^2=a^2 x ...
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Term for candidates for inflection points
The critical points of a function $f(x)$ are candidates for local extrema, i.e., if a function changes from increasing to decreasing, or vice versa, it must happen at a critical point.
Is there an ...
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Finding the Balance in a Math Question (Teaching)
As we try to work and teach in the midst of this pandemic, some problems arise when making online math exams. My question is simple: What could be an interesting basic differentiation question such ...
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Are there direct practical applications of differentiating natural logarithms?
The textbook I am using to teach Calculus I includes in the exercises of most chapters a number of interesting real-world applications of the concepts from that chapter. However, the chapter on the ...
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In single variable calculus, do you distinguish between critical and singular points?
In some texts, a critical point is when the derivative exists and is zero, and a singular point is when the derivative does not exist. So I suppose, at $x=0$, $|x|$ would have a singular point while $...
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A different symbol for the indefinite integral/antiderivative?
Examples. An indefinite integral (or antiderivative) of $\cos$ is $\sin$:
$$\int \cos = \sin.$$
Edit: There has been much unexpected confusion with the above statement. I define the above statement ...
user12641
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Ideas for the introduction of the derivative?
I want to introduce to my class to the derivative, but I am still searching for a good, realistic context that isn't too hard to understand, without seeming to be contrived. Do you have an ideas for ...
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