Derivative of trigonometric functions

[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??

 

[Vagrant]

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

 

[fr33pl4gu3]

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

 

[Vagrant]

Do you know the chain rule?
http://mathworld.wolfram.com/ChainRule.html

 

[fr33pl4gu3]

Is it

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

??

 

[Vagrant]

Yes
And the other?

 

[fr33pl4gu3]

so the answer would be

4cos4x(cos3x) -3 sin4x(sin3x)

Correct??

 

[Vagrant]

Yes.

 

[fr33pl4gu3]

can my last answer be simplify one more step?

 

[Vagrant]

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

 

[Vagrant]

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

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.