Is the chain rule applied in the derivative of cos(t^3) ?

Main Question or Discussion Point

How would you compute the derivative of cos(t^3)? Would you use the chain rule? Does anyone have a good way of recognizing when to use chain rule and when not to?
 

Answers and Replies

quasar987
Science Advisor
Homework Helper
Gold Member
4,771
7
You use the chain rule because it is useful. For instance, here I don't know what the derivative of cos(t³) is. But I know what the derivative of cos(x) is (-sin(x)) and what the derivative of t³ is (3t²). So I choose to make use of the chain rule and say, since cos(t³) is the composition of x-->cos(x) and t-->t³, then

[tex]\frac{d}{dt}(\cos(t^3))=-\sin(t^3)\cdot (3 t^2)[/tex]
 
1,703
5
you use the chain rule anytime you have nested functions. hence if you have a function:

f( g( h( k(x) ) ) ) it's derivative with respect to x is f'( g( h( k(x) ) ) ) * g'( h( k(x) ) ) * h'( k(x) ) * k'(x)
 

Related Threads for: Is the chain rule applied in the derivative of cos(t^3) ?

  • Last Post
Replies
3
Views
6K
Replies
7
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
3
Views
655
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
6
Views
15K
Top