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A visualization for the quotient rule

I really appreciate the area models using differences, but here’s the kind of algebraic manipulation I enjoy, assuming the product rule in place of negative exponents: f'= ((f/g)g)' = (f/g)g'+(f/g)'g ...
Dave Marain's user avatar
7 votes

A visualization for the quotient rule

Here are two geometric ways of thinking about the quotient rule. The first is essentially a geometric interpretation of an algebraic manipulation of the product rule. The second is an interpretation ...
Justin Hancock's user avatar
3 votes

A visualization for the quotient rule

Another option which isn't geometric, but which reinforces the concept of derivative as linear approximation, is as follows. First derive (by any means) that $\frac{\textrm{d}}{\textrm{d}u} \frac{1}{u}...
Steven Gubkin's user avatar
3 votes

A visualization for the quotient rule

If you don't mind using similar triangles and are comfortable with both derivatives positive, you can just set $$ OA=g(x), OC=f(x), CD=XZ=\Delta f(x), AB=ZT=\Delta g(x) $$ and write $$ \frac {f+\Delta ...
fedja's user avatar
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27 votes

A visualization for the quotient rule

Depending on how much algebra you allow, you could make the exact same rectangle picture but label the sides $g(x)$ and $q(x)$ with area $f(x)$. This geometrically enforces $g(x)q(x) = f(x)$, aka $q(...
Steven Gubkin's user avatar
1 vote

How to assess students in real analysis?

I suspect that the rules of assessment are the same for every discipline, calculus not excluded, and can be just derived from first principles and your particular version of common sense without any ...
fedja's user avatar
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