eDiffTrigAll

Example Differntiate the following trig function．

$\displaystyle \displaystyle{y = \tan{3x} + \sec{2x}}$

Answer To find the derivative, it is important to know the following rules.

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. $(\tan{x})' = \sec^{2}{x}, (\sec{x})' = \sec{x}\tan{x}$

Apply these rules to the above problem, we have

$\displaystyle (\tan{3x} + \sec{2x})'$	$\displaystyle =$	$\displaystyle (\tan{3x}5)' + (\sec{2x})'$
	$\displaystyle =$	$\displaystyle 3\sec^{2}{3x} + 2\sec{2x}\tan{2x}$