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

##### 1 Answer

Oct 9, 2016

#### 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)#