Question

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

Answer 1

`y'=(e^x*(cosx+sinx))/(cos^2x)`

Explanation :

let's `y=f(x)/g(x)`

then Using quotient rule to find derivative of above function,

`y'=(f'(x)g(x)-f(x)g'(x))/(g(x))^2`

Similarly following for the given problem,

`y=e^x/cos(x)`, yields

`y'=(e^x*cos(x)-e^x*(-sinx))/(cos^2x)`

`y'=(e^x*(cosx+sinx))/(cos^2x)`