Question

Determine f′(x) for f(x)=ln(19x^11)

Answer 1

isnt it 209x^10/((19x^11)^2)?

Answer 2

substitute u for 19x^11 to get ln(u)
Then derive that like you would normally to get 1/u du
Since u is 19x^11, the derivation for that is 209x^10
Plug in all the numbers to get (209x^10)/(19x^11)

Answer 3

I don't think you need to square the bottom

Answer 4

why isnt it (19x^11)^2?

Answer 5

but the quotient rule needs it to be squared?

Answer 6

Because the derivative of ln(x) is simply 1/x, and the quotient rule isn't used here because that's the answer. Now, if you were deriving it for a second time, you'd have to use the quotient rule but since it's your answer that uses division and not the question, you don't have to use it

Answer 7

ahh okays thank you again