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Eng_physicist
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I need general help in taking the derivative of transformed trig functions is there any formula I can use?
P.S Thanks in advanced
P.S Thanks in advanced
HallsofIvy said:? Without further information, all I can say is the chain rule!
O.K I have to model roller coaster by connecting three functions together the first has to be a polynomial then a trigg function which has to connect with a rational function and the point where they meet it's rate of change can not vary by more than 10%.gb7nash said:Derivatives of trigonometric functions:
http://en.wikipedia.org/wiki/Differentiation_rules#Derivatives_of_trigonometric_functions
Chain Rule:
http://en.wikipedia.org/wiki/Chain_rule
I'm not sure I understand what your question is, but does that clear anything up?
Mark44 said:Please give us some examples of the kind of functions you mean.
Mark44 said:So you have a piecewise-defined function. At the two connection points, the y values have to agree, and you want the derivatives to approximately agree. Assuming that as we go left to right, you have 1) polynomial, 2) trig function, 3) rational function, and these functions are connected at points A and B, you want the derivative of the polynomial to be about the same as the derivative of the trig functions at A, and you want the derivative of the trig function to be about the same as that of the rational function at B.
For numbers to the left of and close to A, use the polynomial function's slope. For numbers to the right of and close to A, use the trig function's slope.
For numbers to the left of and close to B, use the trig function's slope. For numbers to the right of and close to B, use the rational function's slope.
I don't see how that would work. The simplest rational function is y = f(x) = 1/x. You can stretch or compress it vertically by a scaling the y value, as in a*f(x) = a/x. You can stretch or compress it horizontally by a scaling x, as in f(cx) = 1/(cx). I think this is the way to go for your rational function.Eng_physicist said:Is there any particular way to adjust the slope of the rational function
Could I do a reverse derivative by making the slope of the rational function close to that of the trigg function in it's derivative form then turn it back into the non derivative form
A derivative of a transformed trigonometric function is a mathematical concept that represents the rate of change of that function at a specific point. It is calculated by finding the slope of the tangent line at that point.
To find the derivative of a transformed trigonometric function, you can use the chain rule, product rule, quotient rule, or any combination of these rules. It is important to follow the correct order of operations and use the trigonometric identities to simplify the function before taking the derivative.
Some common transformed trigonometric functions include sine, cosine, tangent, secant, cosecant, and cotangent. These functions can be transformed using amplitudes, phase shifts, and frequency changes.
Taking the derivative of transformed trigonometric functions is important in many fields of science and engineering, as it allows us to analyze and understand the behavior of these functions. It is also used in applications such as optimization, curve fitting, and solving differential equations.
Some tips for taking derivatives of transformed trigonometric functions include using the correct rules and formulas, simplifying the function before taking the derivative, and being familiar with the properties of trigonometric functions. It is also helpful to practice and check your work with a calculator or online tool.