Question

lnsqrt (4 x - 5/ 9 x + 9)
Find f'( x )

Answer 1

quotient rule for this one

Answer 2

use
\[(\frac{f}{g})'=\frac{gf'-fg'}{g^2}\] with
\[f(x)=4x-5, f'(x)=4, g(x) = 9x+9, g'(x)=9\]

Answer 3

oh my i ignored the square root part!

Answer 4

ya lol i kind of thought soo, but i didnt say anything cuz i didnt know how to do it anyways

Answer 5

well in that case you still need the derivative of the inside piece

Answer 6

which comes out to
\[\frac{1}{(1+x)^2}\]

Answer 7

so by the chain rule you will have to take the derivative of the square root function first.
\[\frac{d}{dx}[\sqrt{f(x)}=\frac{f'(x)}{2\sqrt{f(x)}}\]

Answer 8

so you should get
\[\frac{\sqrt{9x+9}}{2\sqrt{{4x-5}}}\times \frac{1}{(1+x^2)}\]

Answer 9

can factor out a 3 in the top