Question

find the derivative: r=(2)/(3x − √ 3 )−(ln(x)/9)+ln(9)

Answer 1

i think this might be easier on everyone's eyes if you wrote this using the equation editor

Answer 2

\[r=\frac{2}{3x-\sqrt{3}}-\frac{\ln(x)}{9}+\ln(9)\]?

Answer 3

ln(9) is a constant so it has slope 0 (meaning the derivative of ln(9) is 0)
(lnx)'=1/x
using quotient rule for the first part

Answer 4

I was mistaken it is 3 \[3 \sqrt[3]{x}\]

Answer 5

dont use quotient rule

Answer 6

\[\frac{2}{3*x^{1/3}}=\frac{2}{3}*x^{-1/3}\]

Answer 7

ooh ok I was trying to use the quotient rule...

Answer 8

yeah its just \[\frac{2}{3}*-\frac{1}{3}*x^{-4/3}\]

Answer 9

quotient rule would work and give you the same answer theoretically, but its unnecessary

Answer 10

where did you get \[x ^{4/3}\]

Answer 11

I meant \[x ^{-4/3}\]

Answer 12

\[r=\frac{2}{3\sqrt[3]{x}}-\frac{\ln(x)}{9}+\ln(2)=\frac{2}{3}x^\frac{-1}{3}-\frac{1}{9}*\ln(x)+\ln(2)\]
\[r'=\frac{2}{3}\frac{-1}{3}x^{\frac{-1}{3}-1}-\frac{1}{9}*\frac{1}{x}+0\]

Answer 13

\[r'=\frac{-2}{9}x^{\frac{-1}{3}-\frac{3}{3}}-\frac{1}{9x}\]
\[=\frac{-2}{9}x^\frac{-4}{3}-\frac{1}{9x}\]