How do you find the derivative of y = (2cosx)/(x+1)?

1 Answer
Mar 1, 2017

=((-2)(xsin(x)+sin(x)+cos(x)))/(x^2+2x+1)

Explanation:

Recall that we use the quotient rule to differentiate a function of the form (P(x))/(Q(x)).

The quotient rule states that:
d/(dx)(P(x))/(Q(x))=(Q(x)*P'(x)-P(x)*Q'(x))/(Q(x))^2

I usually remember it as (BT'-TB')/B^2 where T is the top function and B is the bottom function.

Now, applying the quotient rule to the function, we get:

d/(dx)(2cosx)/(x+1)=((x+1)(-2sinx)-(2cosx)(1))/(x+1)^2

=(-2xsin(x)-2sin(x)-2cos(x))/(x^2+2x+1)

or
=((-2)(xsin(x)+sin(x)+cos(x)))/(x^2+2x+1)