Thread: can't differentiate my own equation!

1. can't differentiate my own equation!

hello all, i am in year 12 now and trying to differentiate an equation as proof that my thesis on traffic flow is accurate.
problem is i can't seem to differentiate it.

equation: Y=(1000x)/(4+(0.2x+0.001x^2))

i used some online ones but they wouldn't help me..

if you could attemp to work out Dy/Dx for me i would greatelly appreciate it!

2. Originally Posted by corey0422622443
hello all, i am in year 12 now and trying to differentiate an equation as proof that my thesis on traffic flow is accurate.
problem is i can't seem to differentiate it.

equation: Y=(1000x)/(4+(0.2x+0.001x^2))

i used some online ones but they wouldn't help me..

if you could attemp to work out Dy/Dx for me i would greatelly appreciate it!
I'll start you off

$\displaystyle y = \frac{1000x}{4+.2x+.001x^2}$

$\displaystyle \ln{y} = \ln{\frac{1000x}{4+.2x+.001x^2}}$

$\displaystyle \ln{y} = \ln{1000x} - \ln{(4+.2x+.001x^2)}$

$\displaystyle \frac{y'}{y} = \frac{1000}{1000x} - \frac{.2 + .002x}{4 + .2x + .001x^2}$

3. Originally Posted by corey0422622443
hello all, i am in year 12 now and trying to differentiate an equation as proof that my thesis on traffic flow is accurate.
problem is i can't seem to differentiate it.

equation: Y=(1000x)/(4+(0.2x+0.001x^2))

i used some online ones but they wouldn't help me..

if you could attemp to work out Dy/Dx for me i would greatelly appreciate it!
Use quotient rule:

$\displaystyle f(x)=\dfrac{h(x)}{g(x)}~\implies~f'(x)=\dfrac{g(x) \cdot h'(x)- h(x) \cdot g'(x)}{(g(x))^2}$

$\displaystyle y = f(x)= \frac{1000x}{4+0.2x+0.001x^2}$
$\displaystyle f'(x)= \frac{1000 \cdot (4+0.2x+0.001x^2) - 1000x \cdot (0.2+ 0.002x)}{(4+.2x+.001x^2)^2}$
$\displaystyle f'(x)= \frac{4000-x^2}{(4+.2x+.001x^2)^2}$