How do you use the quotient rule to find the derivative of y=e^x/cos(x) ?

Sep 16, 2014

$y ' = \frac{{e}^{x} \cdot \left(\cos x + \sin x\right)}{{\cos}^{2} x}$

Explanation :

let's $y = f \frac{x}{g} \left(x\right)$

then Using quotient rule to find derivative of above function,

$y ' = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g \left(x\right)} ^ 2$

Similarly following for the given problem,

$y = {e}^{x} / \cos \left(x\right)$, yields

$y ' = \frac{{e}^{x} \cdot \cos \left(x\right) - {e}^{x} \cdot \left(- \sin x\right)}{{\cos}^{2} x}$

$y ' = \frac{{e}^{x} \cdot \left(\cos x + \sin x\right)}{{\cos}^{2} x}$