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)#
