Math Is Fun Forum

baggins

Member

Registered: 2008-06-24

Posts: 5

derivative of the function using the Composite Rule

Hi everyone,

I'm stuck, I'm sure I calculate the function completely wrong. I think cos is right but I don't know how to work the '6x'.
Here is the question and my answer:

    (i) Write down the derivative of the function

                       f(x)= cos(6x).

                         Derivative:

                       f ‘(x)= -sin(6x)
               
                                       
   (ii) Hence, by using the Composite Rule, differentiate the function   

                       k(x) = ecos(6x)

                   Composite rule:       
                                           
                      k ‘(x) = g ‘(f(x)) f ‘(x)                                                            
                               = g ‘(u) f ‘(x)   where u = f(x) = cos(6x)
                                = (eu) (-sin^cos(6x))
                                = e(cos^(6x)) (-sin^cos(6x))
                                = -e sin(^cos(6x))

If someone understand what I did, please help me:/

baggins

Member

Registered: 2008-06-24

Posts: 5

Re: derivative of the function using the Composite Rule

Becarefule I type it wrong, the function 'k(x)' is k(x) = e^cos(6x)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: derivative of the function using the Composite Rule

I find that that way of using the composite rule is confusing, because each ` doesn't tell you what you're differentiating with respect to.

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Why did the vector cross the road?
It wanted to be normal.

baggins

Member

Registered: 2008-06-24

Posts: 5

Re: derivative of the function using the Composite Rule

Thanks again mathsyperson, great help, I need to practise more of them.