Derivatives of Rational Functions

This calculus video tutorial explains how to find the derivative of rational functions. It explains how to use the power rule, chain rule, and quotient rule in order to find the derivative of a fraction.

Equation of the Tangent Line:

Derivatives - Horizontal Tangent Line:

The Equation of The Normal Line:

The Equation of The Secant Line:

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Average and Instantaneous Velocity:

Instantaneous Rate of Change:

Derivatives of Rational Functions:

Derivatives of Radical Functions:

Derivatives of Fractions:

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Derivatives - Higher Order:

Simplifying Derivatives:

Derivatives - The Product Rule:

Derivatives - The Quotient Rule:

Derivatives - The Chain Rule:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

Derivatives - Formula Sheet:

[thobilesikakane]

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[georgesadler]

Professor Organic Chemistry Tutor, thank you for a basic explanation of the Derivative of Rational Functions in Calculus One. I also want to thank the viewers for finding the error in this video at the 4:00 mark.

[baileymerschman]

youre the goat. you get straight to the point with this stuff and make it so much less confusing

[joshc]

There's an error for the derivative of 9/x^2-6....It should be -18x/(x^2-6)^2

[freshinfo]

Bro this taught me more in two minutes than my teacher has in 2 weeks

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[dong-wooklee]

Shortcut for derivative of a function of type: f(x) raised to g(x)
Let f(x) be f
Let g(x) be g
Let derivative of f(x) be f'
Let derivative of g(x) be g'
d/dx(f^g)=(f^g)(f'(g/f)+g' log(f))

For those who couldn't understand what's written above, It reads as:
derivative of f raised to power g is equal to f raised to power g times (derivative of f times g by f + derivative of g into log(f))

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[drewQ]

5 minutes in and I understand rational functions. Amazing

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[Freefranze]

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[nasserrahimi]

I think you dropped x of -18 at 4:03!? It was supposed to be -18x/(x^2-6)^2 to my understanding!

[mfsusrides]

4:34 Can I use qoutient rule to this? Because why he rewrited it? What's the matter?

[annikaj]

At 4:03, shouldn't the answer be -18x/(x^2-6)^2? He even said it was supposed to be -18x but I guess he forgot to write the correct answer