# Using quotient and chain rules for derivatives

• Sep 30th 2009, 10:10 PM
commerce-calc
Using quotient and chain rules for derivatives
Hey so I have a calculus assignment and im not wrapping my head around many of the concepts for derivatives.

My quotient rule question:

a) Use the definition of the derivative to find f'(x) for f(x) = (1/3x-4).
b) Use the result from a) to fi nd the equation of the tangent line to f(x) at the point (2, 1/2 ).

For this I believe I have answered the first part, with

f(x)=(1/3x-4)

f'(x)=(f(x)*g'(x)-f'(x)g(x))/f(x)^2

=-3/(3x^2-24x+16)

I'm don't know what to do to continue to part be.
Thanks very much for any help you might be able to offer.
• Oct 1st 2009, 12:14 AM
creatively12
Quote:

Originally Posted by commerce-calc

=$\displaystyle \frac{-3}{3x^2-24x+16}$

I'm don't know what to do to continue to part be.
Thanks very much for any help you might be able to offer.

Substitute the Point 2 into $\displaystyle \frac{-3}{3x^2-24x+16}$ , which will give you the gradient of the tangent line.

Now, for y-coordinate, subtitute the point x=2 into f(x) i.e. $\displaystyle \frac{1}{3x-4}$, which will give you the y-coordinate.

Then simply put the data into the either 2 formulas Point-Slope or Slope-Intercept, I recommend point-slope.

and there you go, hope you understood
• Oct 1st 2009, 12:24 AM
commerce-calc
awesome. that actually makes sense im not used to that haha.

so i came up with the equation for the tangent line:

y=3/10x-01

sound maybe right? thanks for clearing that up for me :)
• Oct 1st 2009, 12:28 AM
creatively12
Happy to help, just going along these things (Wink)
• Oct 1st 2009, 12:33 AM
creatively12
Quote:

Originally Posted by commerce-calc

=-3/(3x^2-24x+16).

Just noticed this, 3x^2 shouldn't be 3x, it should be 9x^2, correct it, and make the equation again, this time you'll get the right one, sorry for not pointing out earlier (Rock)
• Oct 1st 2009, 12:40 AM
commerce-calc
haha no problem. and thank you very much for noticing the error, fixed and good. thanks again for the help.