`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` .**