I need help differentiating a function

How do you differentiate G(y) = ln [((2y+1)^5)*(sin(y)) / (sqrt(y^2 +1) with respect to y?

ah, log differentiation

remember we can separate logs
ln(a*b) = lna + lnb
ln(a/b) = lna - lnb

so:

g(y) = ln[(2y+1)^5] + ln(siny) - ln[(y^2+1)^(1/2)]

also recall:
ln(a^b) = blna

so:

g(y) = 5ln(2y+1) + ln(siny) - 1/2ln(y^2+1)

from here we just apply the chain rule:

g'(y) = 5[1/(2y+1)](2) + [1/(siny)](cosy) - 1/2[1/(y^2+1)](2y)

simlify:

g'(y) = 10/(2y+1) + coty - y/(y^2+1)

Hope this helps =)

Are you kidding?