Derivative of trigonometric functions

1. Sep 8, 2008

fr33pl4gu3

y = sin( 4 x ) cos( 3 x )

f(x) = sin4x
g(x) = cos3x
f'(x) = cos4x
g'(x) = -sin3x

And by using the product rule, i'll get:

cos4x(cos3x) - sin4x(sin3x)

Is the answer correct or can be simplify again??

2. Sep 8, 2008

Vagrant

Check the f'(x) and g'(x). Are you missing something?

3. Sep 8, 2008

fr33pl4gu3

sin4x can be written in this way (4(sin x)) or not?

Last edited: Sep 8, 2008
4. Sep 8, 2008

5. Sep 8, 2008

fr33pl4gu3

Is it

f'(x)=4cos(4x)

??

Last edited: Sep 8, 2008
6. Sep 8, 2008

Vagrant

Yes
And the other?

7. Sep 8, 2008

fr33pl4gu3

4cos4x(cos3x) -3 sin4x(sin3x)

Correct??

8. Sep 8, 2008

Yes.

9. Sep 8, 2008

fr33pl4gu3

can my last answer be simplify one more step?

10. Sep 8, 2008

Vagrant

Not any that I can think of. It can be re-arranged. Do you have a target answer?

11. Sep 8, 2008

Vagrant

Try to draw the graphs for y= 4 sinx and y=sin4x for x= 0,30,45,60,90 degrees etc. and see for yourself.