# Derivative with Function Math

- Author:
- Dr. Doug Davis, 3D

- Topic:
- Derivative

This is an illustration of derivatives of functions made from arithmetic with other functions. The differentiation rules of constant, constant times a function, sum of functions, difference of functions, product of functions and quotient of functions are all illustrated.
Only one check box can be checked and a new function is created as the sum, difference,product or quotient of the and functions.
The right side graph shows the derivative of the functions. The function values at the point are shown on each graph. The point can be moved on the left graph.
The derivatives of both functions and the new function are shown on the right graph.
The blue fine dashed curve if f(x), the purple dashed line is g(x) and the solid green line is h(x).

Tasks for students:
Click "Next f(x)" until is a constant. Note the derivative of . The constant rule for differentiation is
From this setting check h(x)=f(x)*g(x) to get a constant times the function . Vary the constant and note how the derivative changes. Try this with various g(x) functions.
The constant times a function differentiation rule is
Check the h(x)=f(x)+g(x) to get the sum of function. Verify the rule for differentiating the sum of functions.
Check the h(x)=f(x)-g(x) to get the sum of function. Verify the rule for differentiating the difference of functions.
Check the h(x)=f(x)*g(x) to get the sum of function. Verify the rule for differentiating the product of functions.
Check the h(x)=f(x)/g(x) to get the sum of function. Verify the rule for differentiating the quotient of functions.