Differentiation: Calculation Rules
https://www.maa.org/taxonomy/term/40452/all
enA Note on the Ratio of Arc Length to Chordal Length
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-note-on-the-ratio-of-arc-length-to-chordal-length
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The article illustrates a gap in some not-so-rigorous methods used by authors to use arc length to show the derivative of the sine function is the cosine function.</em></p>
</div></div></div>Constrained Optimization with Implicit Differentiation
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/constrained-optimization-with-implicit-differentiation
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Optimization of \(f(x,y)\), given the constraint \(g(x,y)=0\), can be done using implicit differentiation on both \(f(x,y)\) and \(g(x,y)=0\).</em></p>
</div></div></div>Characterizing Power Functions by Volumes of Revolution
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/characterizing-power-functions-by-volumes-of-revolution
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>The authors characterize power functions by ratios of two specific volumes.</em></div></div></div>An Example Demonstrating the Fundamental Theorem of Calculus
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-example-demonstrating-the-fundamental-theorem-of-calculus
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>A simple example of circular area that exhibits the Fundamental Theorem of Calculus</em></div></div></div>A Bug Problem
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-bug-problem
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>A bug is on the inside of a container that has the shape of a paraboloid \(y=x^2\) revolved about the \(y\)-axis. If a liquid is poured into the container at a constant rate, how fast does the bug have to crawl to stay dry?</em></div></div></div>Logarithmic Differentiation: Two Wrongs Make a Right
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/logarithmic-differentiation-two-wrongs-make-a-right
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Differentiate \(f(x)^{g(x)}\) first as if \(g\) was a constant, then as if \(f\) was a constant. Presto!</em></p>
</div></div></div>An Exponential Rule
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-exponential-rule
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>The author obtains a power rule for derivatives of powers with variable exponents.</i></p>
</div></div></div>A Quotient Rule Integration by Parts Formula
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-quotient-rule-integration-by-parts-formula
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>The rule for differentiation of a quotient leads to an integration by parts formula.</i></p>
</div></div></div>A Useful Notation for Rules of Differentiation
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-useful-notation-for-rules-of-differentiation
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Systematic use of brackets and parentheses to illustrate rules for calculating derivatives</i></p>
</div></div></div>The Computation of Derivatives of Trigonometric Functions
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-computation-of-derivatives-of-trigonometric-functions
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Find the derivative of the arcsine, then the derivative of the sine by using the fundamental theorem of calculus.</i></p>
</div></div></div>A Self-Contained Derivation of the Formula \( \frac {d x^r}{dx}=r x^{r-1}\)
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-self-contained-derivation-of-the-formula-frac-d-xrdxr-xr-1
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><I>Differentiating a power of \(x\) when the power is rational.</I></div></div></div>Differentiate Early, Differentiate Often!
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/differentiate-early-differentiate-often
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Reasons are given for preferring implicit differentiation over eliminating a second variable, then differentiating.</i></p>
</div></div></div>A Note on Differentiation
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-note-on-differentiation
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>A different way to find the product rule</em></p>
</div></div></div>An Area Approach to the Second Derivative
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-area-approach-to-the-second-derivative
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Use area to describe the second derivative of a function</em></div></div></div>The Derivatives of Arcsec \(x\), Arctan \(x\), and Tan \(x\)
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-derivatives-of-arcsec-x-arctan-x-and-tan-x
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Using geometry to find the derivatives of inverse trigonometric functions</em></p>
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