Question

How do you differentiate `f(x)=(x+2)/cosx`?

Answer 1

`f'(x)=(cos(x)+xsin(x)+2sin(x))/cos^2(x)`

Explanation:

To differentiate this, we will use the quotient rule. The quotient rule states that the derivative of a function that is one function divided by another, such as

`f(x)=g(x)/(h(x))`

has a derivative of

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

So, for the given function of

`f(x)=(x+2)/cos(x)`

We can say that

`{(g(x)=x+2),(h(x)=cos(x)):}`

Taking the derivative of both of these, we see that

`{(g'(x)=1),(h'(x)=-sin(x)):}`

Applying these to the quotient rule, this becomes

`f'(x)=(1(cos(x))-(x+2)(-sin(x)))/(cos(x))^2`

Simplifying:

`f'(x)=(cos(x)+xsin(x)+2sin(x))/cos^2(x)`