if sinh(y)=[4sinh(x)-3)/(4+3sinh(x)]

Question

show that
dy/dx=5/(4+3sinh(x)]
step plz i plead

Answer 1

sinh(y)=[(4sinh(x)-3)/(4+3sinh(x))]

cosh(y) y' = (25cosh(x))/(4+3sinh(x))^2

cosh^2(y) = 1+sinh^2(y)
= 25cosh^2(x)/(4+3sinh(x))^2
so,
cosh(y) = 5cosh(x)/(4+3sinh(x))

y' = 5/(4+3sinh(x))