Question

Determine f′(x) for f(x)=(ln(3x))^9.

Answer 1

Have you learned derivatives of logarithmic functions?

Answer 2

yea dont we use chain rule?

Answer 3

ln u = u'/u

Answer 4

If\[y =c [\ln f(x)]^{n}\]then\[\frac{ dy }{ dx }=cn[\ln f(x)]^{n -1}\frac{ f \prime(x) }{ f(x) }\]because\[\frac{ d(\ln f(x)) }{ dx }=\frac{ f \prime(x) }{ f(x) }\]Note that in the above c is a constant.

Does this help?

Answer 5

i dont get it :C

Answer 6

soo 9(ln(3x))^8(3/3x)

Answer 7

Yeah.

Answer 8

ohhh ok ty.