Find dy/dx of y=(cosx)^x

  • Thread starter pugola12
  • Start date
  • #1
5
0

Homework Statement



Find dy/dx of y=(cosx)^x

Homework Equations



d/dx of a^u=lna*a^u*u'

The Attempt at a Solution



I thougt I just had to follow the form shown above, and this is what I got.

y=(cosx)^x
dy/dx=ln(cosx)*(cosx)^x*1
dy/dx=ln(cosx)*(cosx)^x

However, the actual answer is (cosx)^x*(ln(cosx)-xtanx)
I don't understand where this comes from at all. Thanks for your input.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
619

Homework Statement



Find dy/dx of y=(cosx)^x

Homework Equations



d/dx of a^u=lna*a^u*u'

The Attempt at a Solution



I thougt I just had to follow the form shown above, and this is what I got.

y=(cosx)^x
dy/dx=ln(cosx)*(cosx)^x*1
dy/dx=ln(cosx)*(cosx)^x

However, the actual answer is (cosx)^x*(ln(cosx)-xtanx)
I don't understand where this comes from at all. Thanks for your input.

Homework Statement





Homework Equations





The Attempt at a Solution

That's not a good form to follow. It assumes that in a^u that a is a constant. That isn't true in your case. Try writing v^u=e^(log(v)*u) and differentiate that.
 
  • #3
559
8
ln y = x ln cosx

You can now use the product rule on the right side..
(Hint: it becomes (1/y)y' on the left)
 

Related Threads on Find dy/dx of y=(cosx)^x

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
11
Views
10K
Replies
4
Views
5K
  • Last Post
Replies
6
Views
974
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
9
Views
16K
Top