y=tan(ln(2x+1))

Question

Derive

Answer 1

Let u = 2x+1
Let v = ln u
Then y = tan v
dy/dx = (dy/dv)(dv/du)(du/dx)
dy/dx = (sec²v)(1/u)(2)
dy/dx = (sec²(ln (2x+1))(1/(2x+1))(2)
dy/dx = 2sec²(ln (2x+1))/(2x+1)