How to take derivative of transformed trigg functions

[Eng_physicist]

I need general help in taking the derivative of transformed trig functions is there any formula I can use?

P.S Thanks in advanced

 

[HallsofIvy]

? Without further information, all I can say is the chain rule!

 

[Eng_physicist]

? Without further information, all I can say is the chain rule!

Is there any general formula for it when using trigs

 

[Mark44]

Please give us some examples of the kind of functions you mean.

 

[gb7nash]

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?

 

[Eng_physicist]

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?

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%.

 

[Eng_physicist]

Please give us some examples of the kind of functions you mean.

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%
the problem is that I had to transform the trigg function to get it to connect with the Polynomial and rational functions but I don't know how to check it s rate of change where it connects with the rational function

 

[Mark44]

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.

 

[Eng_physicist]

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.

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

 

[Mark44]

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

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.


BTW, "trig" is the usual short form of trigonometry.