Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 29

h(x) = 1/4sinh(2x) - x/2
To take the derivative of this function, refer to the following formulas:
d/dx(u +-v) = (du)/dx+-(dv)/dx
d/(dx)[sinh(u)]=cosh(u)*(du)/dx
d/dx(cu)=c*(du)/dx
d/dx(cx)=c
Applying them, h'(x) will be
h'(x)=d/dx[1/4sinh(2x) - x/2 ]
h'(x)=d/dx [ 1/4sinh(2x)]- d/dx(x/2)
h'(x)=1/4d/dx[sinh(2x)] - d/dx(x/2)
h'(x)=1/4* cosh(2x)*d/dx(2x) - 1/2
h'(x)=1/4*cosh(2x)*2 - 1/2
h'(x)=1/2cosh(2x)-1/2
Therefore, the derivative of the function is h'(x) =1/2cosh(2x)-1/2 .