I have an equation $\displaystyle f(x) = \frac{5x}{(3-5x)^5} $ and I want the equation of the tangent line at x = 2. I know what to do, but my math is wrong somewhere down the line.

Subbing in 2 $\displaystyle f(2) = \frac{5(2)}{(3-5(2))^5} = -0.000595 $

Taking derivative $\displaystyle f'(x) = \frac {100x+15}{(3-5x)^6} $ and then plugging in 2 $\displaystyle f'(2) = \frac {100(2)+15}{(3-5(2))^6} = 0.00183 $

So, I use equation of a line now that I have the solutions for f(x) and m.... $\displaystyle -0.000595 = 0.00183(2) + b $ and I wind up with $\displaystyle b = 0.0043 $

I get the equation of the tangent line should be $\displaystyle y = 0.00183x + 0.0043 $ ,but this is incorrect, and I was hoping somebody could eyeball this if they get a chance because I think I'm going in circles trying to fix it.