Hello there. I'm new to this forum so I apologise in advance if what I have posted seems a little unclear to you. I just need a little help with the following question.
If, sinhy = (4sinhx - 3) / (4 + 3sinhx)
show that,
dy/dx = -5 / (4 + 3sinhx)
My final answer contains coshy, and I do not know where to go from there to get the above.
Thanks in advance.
That's a very valid point. Okay so these are the steps I took (keeping in mind I used the quotient rule).
differentiating w.r.t x we get the following,
cosh(y) dy/dx = [(4 + 3sinh(x))(4cosh(x)) - (4sinh(x) - 3)(3cosh(x)] / (4 + 3sinh(x))^2
open up the numerator to get,
cosh(y) dy/dx = 25cosh(x) / (4 + 3sinh(x))^2
thus,
dy/dx = 25cosh(x) /cosh(y) (4 + 3sinh(x))^2