Logarithmic Differentiation of (x+5)(x+9): Where Did I Go Wrong?

[vysero]

Homework Statement

Find the derivative using logarithmic differentiation:
y=(x+5)(x+9)

The Attempt at a Solution

lny=ln(x^2+14x+45)
lny=(2x+14)/(x^2+14x+45)
y'=(x^2+14x+45)((2x+14)/(x^2+14x+45))However, I know the derivative of the function is actually 2x+14. So I am wondering what is wrong with my process?

UPDATE: Wow it only took typing my problem into this forum and making the post before I realized that I did do it right! You guys are good! lol sorry for wasting any ones time.

 

[STEMucator]

Homework Statement

Find the derivative using logarithmic differentiation:
y=(x+5)(x+9)

The Attempt at a Solution

lny=ln(x^2+14x+45)
lny=(2x+14)/(x^2+14x+45)
y'=(x^2+14x+45)((2x+14)/(x^2+14x+45))However, I know the derivative of the function is actually 2x+14. So I am wondering what is wrong with my process?

UPDATE: Wow it only took typing my problem into this forum and making the post before I realized that I did do it right! You guys are good! lol sorry for wasting any ones time.

Why wouldn't you just say :

lny=ln((x+5)(x+9))
ln y = ln(x+5) + ln(x+9)

Now...

y'/y = Take the derivative here

Would've been muchhhh easier.