The Chain Rule

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.

• 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.

•

d/dx[f(g(x))] = f `(g(x)) • g `(x)

Also known as:

(derivative of the outside function) • (derivative of the inside function)

• U- Substitution• Where dy/dx = dy/du • du/dx

• In which du/dx = u`

3 is a constant in which case tan(x)

would be the outside function and is the inside function.

• 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.