# Double Check Trig Derivative Question

• April 14th 2009, 04:57 PM
mike_302
Double Check Trig Derivative Question
The function is: $f(x)=2*cos^3x+cos^4x$

My derivative is:
$f'(x)=-sin(2x)cos(x)(3+2*cos(x))$

The back gives a totally different answer... I want to confirm mine.
• April 14th 2009, 05:36 PM
nzmathman
Differentiate $2\cos^3{x}$ and you get $-6\cos^2{x}\sin{x} = -3\sin{2x}\cos{x}$

Differentiate $\cos^4{x}$ and you get $-4\cos^3{x}\sin{x} = -2\sin{2x}\cos^2{x}$

$f'(x) = -3\sin{2x}\cos{x} - 2\sin{2x}\cos^2{x} = -\sin{2x}\cos{x}\,(3+2\cos{x})$