eDiffTrigonometry

Example Find the derivative of the following function．

$\displaystyle \displaystyle{y = \sin{3x} + \cos{2x}}$

Answer To find the derivative of trig function, it is important to know the followings:

1. The derivative of a sum is the sum of the derivatives．
2. The derivative of a constant multiple is the constant times the derivative． $(\alpha f(x))' = \alpha f'(x)$
3. Basic formula for derivatives． $(\sin{x})' = \cos{x}, (\cos{x})' = -\sin{x}$

We apply these rules to the above problem. Then we have

$\displaystyle (\sin{3x} + \cos{2x})'$	$\displaystyle =$	$\displaystyle (\sin{3x})' + (\cos{2x})'$
	$\displaystyle =$	$\displaystyle 3\cos{3x} - 2\sin{2x}$