Differentiation?

Question

Given that y = In ( 1 + 4x / 1 - 4x) and that dy / dx = k / (1 - 16x^2), find the numerical value of k.

Hence, find the equation of normal to the curve at the point where x = 1/5

Answer 1

y' = 4/(1+4x) - -4/(1-4x)
y' = [4(1-4x)+4(1+4x)]/[1-16x^2]
y' = 8/[1-16x^2]
So k = 8
When x = 1/5, y = 2.197
When x = 1/5 y' = 22 2/9 = =200/9
So normal will have slope of -9/200
Equation is y= -9x/200 +b
2.197 = -9/1000 --> b = 2.206
So y = -9x/200 +2.206