# 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.