Derivative of x sqrt(6x - 1)

Apr 2010
26
0
Australia
1st
\(\displaystyle f(x)=x(6x-1)^\frac{1}{2} \)

so what is the derivative? ive nevewr used the function of a fnction with an x out the front.

thankyou

also does anyone know where i can find a lot of calculus question (im in year 11) or trig questions as i have an exam in 2 days that i really need to go well in
 
Last edited by a moderator:
Mar 2010
715
381
Use the product rule \(\displaystyle \left[f(x)\cdot f(x)\right]' = f'(x)\cdot g(x)+g'(x)\cdot f(x)\) then the chain rule for the 'function of a function' part.
 
May 2008
400
82
Ottawa, Canada
use the product rule. (f.g)=f'g+g'f

\(\displaystyle f'(x)=1(6x-1)^{\frac{1}{2}}+x \frac{1}{2}(6x-1)^{\frac{-1}{2}}(6)\)

\(\displaystyle f'(x)=1(6x-1)^{\frac{1}{2}}+x 3(6x-1)^{\frac{-1}{2}}\)