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The Chain Rule

The Chain Rule. Gottfried Wilhelm von Leibniz 1646 - 1716.

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The Chain Rule

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  1. The Chain Rule

  2. Gottfried Wilhelm von Leibniz1646 - 1716 • Gottfried Leibniz was a German mathematician who developed the present day notation for the differential and integral calculus. His theories of calculus and differentials led to the inspiration of rules such as the chain rule to derive functions.

  3. What is a derivative? • The derivative is a particular type of limit also known as the rate of change. • It takes on y- values for specific values of x • It is a function therefore it can be graphed • The derivative of a function is the slope of a line tangent to the function at a particular point.

  4. What does a derivative look like? the red line is the derivative of the blue function

  5. How The Chain Rule Works d/dx[f(g(x))] = f `(g(x)) • g `(x) Also known as: (derivative of the outside function) • (derivative of the inside function)

  6. You Can Also use… • U- Substitution • Where dy/dx = dy/du • du/dx • In which du/dx = u`

  7. Example 1

  8. Let's try some Trig...

  9. Well...that was just a warm up... 3 is a constant in which case tan(x) would be the outside function and is the inside function.

  10. Lets try that using U-Substitution.

  11. Now that you've got that down, let's try another!

  12. ...just one more.

  13. How will this help me in the future? • The chain rule is useful to derive all sorts of derivatives. If you choose to be a math teacher or architect you may need to know how to derive equations in order to teach them and also know the slope tangent line to things so you can be precise in architectural work.

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