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17Calculus - Invalid Derivative Quotient Rule

17Calculus
Single Variable Calculus
Derivatives
Integrals
Multi-Variable Calculus
Precalculus
Functions

As you know, the quotient rule for taking the derivative is \[ \left[ \frac{f(x)}{g(x)} \right]' = \frac{f'g-fg'}{g^2} \] One of the most common mistakes students do when first learning this rule is to take the derivative of each function and then divide the results. The correct equation is based on limits.

When does \(\displaystyle{ \left[ \frac{f(x)}{g(x)} \right]' = \frac{f'(x)}{g'(x)} }\) hold?

It would be nice if we could take the derivative of each function and then just divide \(g'\) into \(f'\). But this will not work nearly all the time. This video shows that this invalid quotient rule works only in a couple of special cases.

Michael Penn - Let's change the quotient rule!

video by Michael Penn

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