Derivative of the following: cospix^2/(x+2)

Question

I am looking for the derivative, using chain rule and quotient rule of the following function:

cospix^2/(x+2)

Answer 1

Given CosPix^2/(x+2)

Remember the derivative of Cosx = -Sinx

For this function apply chain rule.

CosPix^2/(x+2)

Apply dervative with respectof x.

= d/dx[CosPix^2/(x+2)]

= -piSinpi[d/dx(x^2/(x+2)]

Apply the quotient rule in derivatives.

= -piSinpi[((x+2)2x-x^2(1))/(x+2)^2

= -piSinpi[(2x^2+4x-x^2)/(x+2)^2

= -piSinpi[(x^2+4x)/(x+2)^2

Answer 2

is the required answer.