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# Derivatives

You can plot a function and a secant line.

You can plot a function and secant lines tending toward a tangent line.

You can evaluate a derivative using its definition as a limit.

You can evaluate a derivative.

You can define a function, take its derivative, and plot both. Try changing to f(x)=(x-1)^2*sqrt(x) to see what happens. Then try f(x)=(x^5+x^3+2)/(8*x+1) ; change the interval to try to determine f'(0).

You can evaluate the derivative of a product with a manual product rule.

You can evaluate the derivative of a quotient with a manual quotient rule.

You can evaluate the derivative of a composition with a manual chain rule.

You can plot an implict curve $$f(x,y)=0$$. Try it for f(x,y)=2*y^3+y^2-y^5-x^4+2*x^3-x^2.

You can compute an implicit derivative.

You can evaluate a derivative involving exponentials, logs, hyperbolic functions, inverse trigonometric functions, ....

You can gather information to graph.

You can do Newton's method. Try setting p=0.5 and then p=3.0. Now try with f(x) = ((x-3/4)^(1/3))/(x^(1/3)) and p=0.1.

Martin J. Mohlenkamp