Derivative of f(x) = cos pi*x

  • #1
How would I do the derivative of

f(x) = cos pi*x

I know f'(x) cos x = - sin x but what about that pi?
 

Answers and Replies

  • #2
Are you familiar with the chain rule ?
 
  • #3
James R
Science Advisor
Homework Helper
Gold Member
601
15
The chain rule is

[tex]\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}[/tex]

Take y = cos u

then you know that dy/du = -sin u.

Now put u = nx, for n a constant.

You know that du/dx = n

Now consider:

y = cos nx

Put u = nx, so that y = cos u. Then the chain rule tells us:

[tex]\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}[/tex]
[tex]= (-\sin u)(n)[/tex]
[tex]= -n\sin nx[/tex]
 

Related Threads on Derivative of f(x) = cos pi*x

Replies
2
Views
2K
  • Last Post
Replies
4
Views
2K
Replies
15
Views
2K
  • Last Post
Replies
4
Views
99K
Replies
1
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
Replies
2
Views
1K
Replies
5
Views
28K
Replies
4
Views
1K
Top